Sz\303\241m\303\255t\303\263g\303\251pes sz\303\241melm\303\251let J\303\241rai Antal Ezek a programok csak szeml\303\251ltet\303\251sre szolg\303\241lnak
<Text-field style="Heading 1" layout="Heading 1"><Font encoding="UTF-8">1. A pr\303\255mek eloszl\303\241sa, szit\303\241l\303\241s</Font></Text-field>
<Text-field style="Heading 1" layout="Heading 1"><Font encoding="UTF-8">2. Egyszer\305\261 faktoriz\303\241l\303\241si m\303\263dszerek</Font></Text-field>
<Text-field style="Heading 1" layout="Heading 1"><Font encoding="UTF-8">3. Egyszer\305\261 pr\303\255mtesztel\303\251si m\303\263dszerek</Font></Text-field> LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn
<Text-field style="Heading 1" layout="Heading 1">4. Lucas-sorozatok</Text-field>
<Text-field style="Heading 1" layout="Heading 1"><Font encoding="UTF-8">5. Alkalmaz\303\241sok </Font></Text-field> restart; with(numtheory); 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
<Text-field style="Heading 2" layout="Heading 2">5.1. Fermat-sz<Font encoding="UTF-8">\303\241</Font>mok.</Text-field>
<Text-field style="Heading 2" layout="Heading 2">5.2. Feladat.</Text-field>
<Text-field style="Heading 2" layout="Heading 2">5.3. Feladat.</Text-field> interface(verboseproc=2); IiIi print(fermat); Zio2JCdJIm5HNiItSSNPckdGJjYkSSpub25uZWdpbnRHJSpwcm90ZWN0ZWRHLUkkTm90R0YmNiNJKWNvbnN0YW50R0YrSSZfaW5mb0dGJjYkSSJmR0YmSSVpbmZvR0YmNiNJYW9Db3B5cmlnaHR+KGMpfjE5OTJ+Ynl+dGhlflVuaXZlcnNpdHl+b2Z+V2F0ZXJsb28ufkFsbH5yaWdodHN+cmVzZXJ2ZWQuR0YmRiZAKS8lJm5hcmdzRyIiIU82JC1JJGNhdEdGKzYkSUpUaGV+cHJpbWFsaXR5fmNoYXJhY3Rlcn5vZn50aGV+Zm9sbG93aW5nfkdGJklCRmVybWF0fm51bWJlcnN+aXN+a25vd25+dG9+TWFwbGU6R0YmLUklc29ydEdGKzYjLUkoY29udmVydEdGKzYkSTVrbm93bl9mZXJtYXRfbnVtYmVyc0dGJi5JJWxpc3RHRistSSV0eXBlR0YrNiRGJS5JJW5hbWVHRitPLCYpIiIjKUZSRiUiIiJGVEZULUZLNiRGJS5GKkMlQCc0LUknbWVtYmVyR0YrNiRGJUZHT0kyY2hhcmFjdGVyfnVua25vd25HRiY1MkYlIiNBL0ksX0VudlRyeUhhcmRHRiZJJXRydWVHRis+RjJGUD5GMkkvb2JqZWN0fnRvb35iaWdHRiZAJC9GOEZSQD0xRiUiIiU+RjBJLGl0fmlzfnByaW1lR0YmL0YlIiImPkYwNiRJO2l0fmlzfmNvbXBsZXRlbHl+ZmFjdG9yZWR+R0YmKiYtSSFHRiY2IywmLUkoaWZhY3RvckdGJjYjIiRTJ0ZURlRGVEZULUZhcDYjLCYtRmVwNiMiKDsvcSdGVEZURlRGVC9GJSIiJz5GMDYkRl5wKiYtRmFwNiMsJi1GZXA2IyInd1RGRlRGVEZURlQtRmFwNiMsJi1GZXA2IyIvPzJKQC9HbkZURlRGVEZUL0YlIiIoPkYwNiRGXnAqJi1GYXA2IywmLUZlcDYjIjI7c1xGIiplXCdmRlRGVEZURlQtRmFwNiMsJi1GZXA2IyI3P1owSF5vKyMqby9kRlRGVEZURlQvRiUiIik+RjA2JEZecComLUZhcDYjLCYtRmVwNiMiMScqR2JoaiMqUTdGVEZURlRGVCwmKiYpLUZhcDYjRlIiIzZGVC1GYXA2IyJmbjp4d0AheTNMbzdvc1whPTpfT1IqZiNlUFlFbmljTmMlRlRGVEZURlRGVC9GJSIiKj5GMDYkRl5wKigtRmFwNiMsJi1GZXA2IyIoS1tVI0ZURlRGVEZULCYqJi1GYXA2IyJPKGYhPjckeSRHbSI9LFdBNWg0KTNAbjVWU09GVEZddEZURlRGVEZURlQsJiomLUZhcDYjIltxMiRwbGpAR0JVbmxxdl1TT185Vl4iKjMnSEY/JmYvJGVEMmEhPWpyXC0jPUMhXClIbyQqR0BPRlRGXXRGVEZURlRGVEZUL0YlIiM1PkYwNiRGXnAqKi1GYXA2IywmLUZlcDYjIil3RGZYRlRGVEZURlQtRmFwNiMsJi1GZXA2IyIrMz0uKFsnRlRGVEZURlQsJiomLUZhcDYjIkZeIUhfOyslKj5rJyozIltqRGRTdzgiRlQpRl50IiM3RlRGVEZURlRGVCwmKiYtRmFwNiMsJiomI0ZUImluS3dCJGU3MEwrSCdcLkl3OFxfZk1hKUhdJkdVayM0LiFINkZURjJGVEZUI0ZUIiUjPikhIiJGVClGXnQiIzhGVEZURlRGVEZUL0YlRmB0PkYwNiRGXnAqLC1GYXA2IywmLUZlcDYjIicpWz4kRlRGVEZURlQtRmFwNiMsJi1GZXA2IyInW1soKkZURlRGVEZULCYqJi1GYXA2IyIyejdgJXkyS0Q1RlQpRl50IiM5RlRGVEZURlRGVCwmKiYtRmFwNiMiMzYoUUhHJTN0WVZGVEZceEZURlRGVEZURlQsJiomLUZhcDYjLCYqJiNGVCJlbnMjKSo0NGw9cylIMk0uTXUsRyNSVzVTSXdQcmM5aV8iRlRGMkZURlRGaXdGW3hGVEZceEZURlRGVEZURlQvRiVGZHk+RjBJMWl0fmlzfmNvbXBvc2l0ZX5HRiYvRiUiIz8+RjBJMGl0fmlzfmNvbXBvc2l0ZUdGJi9GJUZcb0Znei9GJSIjQ0ZnekZlbkMkQCUtSSlhc3NpZ25lZEdGKzYjJkkrZmVybWF0X3RhYkdGJjYjRiU+RjNGYVtsWVFGbnVtYmVyfnJlY29nbml6ZWR+YnV0fm5vfmZhY3Rvcn5rbm93bkYmPkYwNiQtSSNpZkdGKzYlLy1JJW5vcHNHRis2I0YzRlRJOml0fmhhc350aGlzfnByaW1lfmZhY3Rvcn5HRiZJPGl0fmhhc350aGVzZX5wcmltZX5mYWN0b3JzfkdGJi1JI29wR0YrRl9cbE9JQ25vfmNvbXBsZXRlfmZhY3Rvcml6YXRpb25+aXN+a25vd25HRiZPRjIuLSUpcHJvY25hbWVHNiMlJWFyZ3NHRiZGJjYmRkdGR0ZiW2xGYlts
<Text-field style="Heading 2" layout="Heading 2">5.4. Mersenne-sz<Font encoding="UTF-8">\303\241</Font>mok.</Text-field> mersennes:=[2,3,5,7,13,17,19,31,61,89,107,127,521,607,1279,2203,2281,3217,4253,4423,9689,9941,11213,19937,21701,23209,44497,86243,110503,132049,216091,756839,859833,1257787,1398269,2976221,3021377,6972593,13466917,20996011,24036583,25964951,30402457,32582657,37156667,42643801,43112609]; N1EiIiMiIiQiIiYiIigiIzgiIzwiIz4iI0oiI2giIyopIiQyIiIkRiIiJEAmIiQyJyIlejciJS5BIiUiRyMiJTxLIiVgVSIlQlciJSpvKiIlVCoqIiY4NyIiJlAqPiImLDwjIiY0SyMiJihcVyImVmkpIicuMDYiJ1w/OCInIjQ7IyInUm92IidMKWYpIigoeWQ3IihwIylSIiIoQGkoSCIoeDgtJCIoJGZzcCIpPHBZOCIpNmcqNCMiKSRlT1MjIileXCdmIyIpZENTSSIpZEVlSyIpbm06UCIpLFFrVSIpNEU2Vg==
<Text-field style="Heading 2" layout="Heading 2">5.5. Feladat.</Text-field>
<Text-field style="Heading 2" layout="Heading 2">5.6. Feladat.</Text-field> interface(verboseproc=2); IiIj print(mersenne); 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
<Text-field style="Heading 2" layout="Heading 2">5.7. h*2^m+-1 alak<Font encoding="UTF-8">\303\272</Font> pr<Font encoding="UTF-8">\303\255</Font>mek keres<Font encoding="UTF-8">\303\251</Font>se.</Text-field>
<Text-field style="Heading 2" layout="Heading 2">5.8. Feladat.</Text-field>
<Text-field style="Heading 2" layout="Heading 2">5.9. Feladat.</Text-field>
<Text-field style="Heading 2" layout="Heading 2">5.10. Ikerpr<Font encoding="UTF-8">\303\255</Font>mek.</Text-field>
<Text-field style="Heading 2" layout="Heading 2">5.11. Feladat.</Text-field>
<Text-field style="Heading 2" layout="Heading 2">5.12. Feladat.</Text-field>
<Text-field style="Heading 2" layout="Heading 2">5.13. Sophie Germain pr<Font encoding="UTF-8">\303\255</Font>mek.</Text-field>
<Text-field style="Heading 2" layout="Heading 2">5.14. Ikerpr<Font encoding="UTF-8">\303\255</Font>m, amely Sophie Germain pr<Font encoding="UTF-8">\303\255</Font>m is.</Text-field>
<Text-field style="Heading 2" layout="Heading 2">5.15. n^2+1 es n^4+1 alak<Font encoding="UTF-8">\303\272</Font> pr<Font encoding="UTF-8">\303\255</Font>mek.</Text-field>
<Text-field style="Heading 2" layout="Heading 2">5.16. Egy<Font encoding="UTF-8">\303\251</Font>b speci<Font encoding="UTF-8">\303\241</Font>lis alak<Font encoding="UTF-8">\303\272</Font> pr<Font encoding="UTF-8">\303\255</Font>mek.</Text-field>
<Text-field style="Heading 2" layout="Heading 2">5.17. K<Font encoding="UTF-8">\303\241</Font>tai egy probl<Font encoding="UTF-8">\303\251</Font>m<Font encoding="UTF-8">\303\241</Font>ja.</Text-field>
<Text-field style="Heading 2" layout="Heading 2">5.18. P<Font encoding="UTF-8">\303\251</Font>lda.</Text-field> # # This is a simple factorization # procedure using trial division. # The result is a sequence of pairs # [p,e] where the p's are the prime # factors and the e's are the exponents. # The factors are anyway in increasing order. # Only primes <= P are tried, hence the # last "factor" may composite, if # it is greater then P^2; # trialdiv:=proc(n::posint,P::posint) local L,p,i,d,nn; L:=[]; nn:=n; if type(nn,even) and 2<=P then for i from 0 while type(nn,even) do nn:=nn/2; od; L:=[[2,i]]; fi; if nn mod 3=0 and 3<=P then for i from 0 while nn mod 3=0 do nn:=nn/3; od; L:=[op(L),[3,i]]; fi; d:=2; p:=5; while p<=P and nn>=p^2 do if nn mod p=0 then for i from 0 while nn mod p=0 do nn:=nn/p; od; L:=[op(L),[p,i]]; fi; p:=p+d; d:=6-d; od; if nn>1 then L:=[op(L),[nn,1]] fi; L; end; Zio2JCdJIm5HNiJJJ3Bvc2ludEclKnByb3RlY3RlZEcnSSJQR0YmRic2J0kiTEdGJkkicEdGJkkiaUdGJkkiZEdGJkkjbm5HRiZGJkYmQys+Riw3Ij5GMEYlQCQzLUkldHlwZUdGKDYkRjBJJWV2ZW5HRigxIiIjRipDJD8oRi4iIiEiIiJGJkY3PkYwLCQqJiNGQEY8RkBGMEZARkA+Riw3IzckRjxGLkAkMy8tSSRtb2RHRiY2JEYwIiIkRj8xRk5GKkMkPyhGLkY/RkBGJkZKPkYwLCQqJiNGQEZORkBGMEZARkA+Riw3JC1JI29wR0YoNiNGLDckRk5GLj5GL0Y8PkYtIiImPyhGJkZARkBGJjMxRi1GKjEqJClGLUY8RkBGMEMlQCQvLUZMNiRGMEYtRj9DJD8oRi5GP0ZARiZGYW8+RjAqJkYwRkBGLSEiIj5GLDckRlg3JEYtRi4+Ri0sJkYtRkBGL0ZAPkYvLCYiIidGQEYvRmhvQCQyRkBGMD5GLDckRlg3JEYwRkBGLEYmRiZGJg== trialdiv(2^107-2^54+1,1000); NyU3JCIiJiIiIjckIiRkKUYlNyQiPihSYCM+VUVkK21oITRvJ3kkRiU= n0:=%[3][1]; Ij4oUmAjPlVFZCttaCE0byd5JA== modp(3&^(n0-1),n0); IiIi trialdiv(n0-1,1000); Nyc3JCIiI0YkNyQiIz4iIiI3JCIkMiJGJzckIiRgJEYnNyQiOCwkXGdBM1R2cTc+OEYn n1:=%[5][1]; IjgsJFxnQTNUdnE3Pjg= modp(3&^(n1-1),n1); IjgqeTNTTzo/JTNMWUIi trialdiv(n1,100000); NyQ3JCImOD0qIiIiNyQiM3hwPmRPVHZPOUYl n2:=%[2][1]; IjN4cD5kT1R2Tzk= modp(3&^(n2-1),n2); IiIi trialdiv(n2-1,1000); NyY3JCIiIyIiJTckIiIkRiQ3JCIkWiYiIiI3JCIuZGF4S1MjPUYq n3:=%[4][1]; Ii5kYXhLUyM9 modp(3&^(n3-1),n3); Ii5Gc0RfeV8i trialdiv(n3,10000); NyQ3JCIlLjYiIiI3JCIrPjpxYDtGJQ== n4:=%[2][1]; Iis+OnFgOw== modp(3&^(n4-1),n4); IiIi trialdiv(n4-1,1000); Nyg3JCIiIyIiIjckIiIoRiU3JCIjPkYlNyQiI0JGJTckIiRQIkYlNyQiJXQ+RiU= trialdiv(2^107+2^54+1,1000); NyM3JCJCOCx4PmwoZlMiUTgjSG9GZkE7IiIi n5:=%[1][1]; IkI4LHg+bChmUyJROCNIb0ZmQTs= modp(3&^(n5-1),n5); IkEkZWEqKkg8dkpfcC1nJnpUT1Y= trialdiv(2^107+2^54+1,1000000); NyQ3JCInKmVWKSIiIjckIjw8PlwnNCRIeC05JCpSTSM+RiU= n6:=%[2][1]; Ijw8PlwnNCRIeC05JCpSTSM+ modp(3&^(n6-1),n6); IjwnUT4wQE1dO1l2KmVxIj0=
<Text-field style="Heading 2" layout="Heading 2">5.19. Feladat.</Text-field>
<Text-field style="Heading 2" layout="Heading 2">5.20. Pr<Font encoding="UTF-8">\303\255</Font>msz<Font encoding="UTF-8">\303\241</Font>mk<Font encoding="UTF-8">\303\263</Font>dol<Font encoding="UTF-8">\303\241</Font>s.</Text-field>
<Text-field style="Heading 2" layout="Heading 2">5.21. Feladat.</Text-field> p:=safeprime(1563456788814256178886765661555261342987645321345665432123456788772091275121098761232122333321233434123432123344454321234320948725467845467788859812342365); log[2.](p); q:=safeprime(29841524475159001676561453467890987651234254321456490998767626788182514325678909987236514234154232396587874778993377722004988376667882767156363888377626677728888); log[2.](q); n:=p*q; e:=2876354132453678909987653432123409887635423125; igcdex(e,(p-1)*(q-1),'d'); d; d*e mod (p-1)*(q-1); ImV0ekpPNylmKSl5bmEleVlEKFs0S003S2FXTUJAVkJUVkw3S0xCN0s3dyk0QF5GIjRzKCl5Y003S2FtWDhLWHcpSE1oX2JoY3cnKSl5aEQ5KSl5Y01jIg== JCIrenQqKikzJiEiKA== Ilx1Rk4heW5Fd1ApKVFPY3J3Iyl5bXckKSlcK0F4UCQqKnlaKHllJ1JLVTpNVV5PcykqNCp5Y0s5RD0peUV3dykqNFxjOUthVUJedyk0KnlZYDljdzsrZl5aQzolKUg= JCIrayJlM0wmISIo ImVebExCOEpcUGg+W1AtRnBSbS5rPUVAZUkieW4ocGZNJVFiKEdqQEVjZDFyO0FHcmViNWxbcHltbm9FUExoSjR4IjMjcCNvTlYxXmpHKDNdKnlWIUcleW0hKTM6RDoqPVA7Njkob15KKVswbW9BJVtMYVwuJWZ1Smw2QS0nUmQ0ITQ1V1VQZ3VFaVgqPjVOYCVcTSJ5S3RGKkc2cy9Td1tBIz1DQ1RESFMkZmxZ Ik9ESlVOdykpNE03S01sKCkqNCp5T1hLVE53Rw== IiIi IWVebEpRWytVOSpvSzIzZyYpekp2P0Z0O0RsLzc1IW9WUHJvOlsncE8tVWUqMyk0Q0s9ZGxIOjNYXEJNOnlpLStrOFNeJypbPiNmJyo+cipIW1UqZmRNS3NCMmVyJCp5JlEnb05GQlQzS1xAI29TL2tNVXAneTw7KFwxUydIQjolZWEkRzEjPU9eN24/YiV5JykpPmtANihcSipSI3ooKltMOl1zRGQ2bVAnR3lDaUhyJj4= IiIi
<Text-field style="Heading 2" layout="Heading 2">5.22. Feladat.</Text-field> M:="Mint v\303\255z alatti, elmer\303\274lt harangok hint\303\241znak-e hajnalonk\303\251nt \303\241gyadn\303\241l a tizennyolc \303\251ves iskol\303\241sok kiket felakasztatt\303\241l"; convert(M,'bytes'); m:=sum(%[i]*256^(i-1),i=1..nops(%)); c:=m&^e mod n; UVx0TWludH5gdnxed3xodXpgfmFsYXR0aSx+YGVsbWVyfF53fGd2bHRgfmhhcmFuZ29rfCt8K2BoaW50fF53fFx1em5ha2AtZX5gaGFqbmFsb25rfF53fGR1bnRgfmB8Xnd8XHVneWFkbnxed3xcdWxgfCt8K2F+dGl6ZW5ueW9sY35gfF53fGR1dmVzYH5gaXNrb2x8Xnd8XHVzb2tgfCt8K2tpa2V0fmBmZWxha2FzenRhdHR8Xnd8XHVsYDYi N11zIiN4IiQwIiIkNSIiJDsiIiNLIiQ9IiIkJj4iJHQiIiRBIkYnIiMoKiIkMyJGLEYmRiZGJCIjV0YnIiQsIkYtIiQ0IkYvIiQ5IkYpIiQpPUYtRiZGJyIkLyJGLEYxRixGJSIkLiIiJDYiIiQyIiIjNUY3RjNGJEYlRiZGKSIkaCJGK0YlRixGNiIjWEYvRidGM0YsIiQxIkYlRixGLUY1RiVGNkYpIiRwIkYlRiZGJ0YpRjhGNCIkQCJGLCIkKyJGJUYpRjhGLUY3RjdGLEYnRiZGJEYrRi9GJUYlRjxGNUYtIiMqKkYnRilGO0YoRi8iJDoiRidGJEY/RjZGNUYtRilGOEY/RjVGNkY3RjdGNkYkRjZGL0YmRiciJC0iRi9GLUYsRjZGLEY/RitGJkYsRiZGJkYpRjhGLQ== ImJebCQqKT1jbCJ6JilvaDdJbCp6cUpuIilcYFtSeFZ4W3BmRmAoNHlcJipbIWZ3Kls1NClvREo6IXB4I3lyLUR6JG9AW2IzPEpTKlEiKj5BdTVHNm4qZiUpPl1ETkRKUSJmSVdmNFkoPmlvYSpHRU90XTUzRylIeWEiW3glUkpjLGFxYE4zQ3lWdWghcDZBdDdFQjZAVFkleSpRI2VNI1JnNCo9NnVTMDYxQ1krb0cmPg== ImNebD1LYlAoKilbQ1Y6JSlbJ2VFSyJRS0xbVDwiSDxrRlYpZiE+NzAmMyVIJ3lmOikzd2h3MWtQSjI+aTZKWk1cMS0vJylmZExYTihvR0hJemp6Z3VfNT8qcENaKDRVKG9pQXBGWlohelwxUlklW0AiPWtyMU0rJ0dxXi9BMEldIT0oKUhcWTEmRzcmXG1zOlFvdC9fZCNcZSkqKTRNUTxKISkpb15vdllFKXBBJVxbX3g= c&^d mod n; convert(%,base,256); convert(%,'bytes'); ImJebCQqKT1jbCJ6JilvaDdJbCp6cUpuIilcYFtSeFZ4W3BmRmAoNHlcJipbIWZ3Kls1NClvREo6IXB4I3lyLUR6JG9AW2IzPEpTKlEiKj5BdTVHNm4qZiUpPl1ETkRKUSJmSVdmNFkoPmlvYSpHRU90XTUzRylIeWEiW3glUkpjLGFxYE4zQ3lWdWghcDZBdDdFQjZAVFkleSpRI2VNI1JnNCo9NnVTMDYxQ1krb0cmPg== N11zIiN4IiQwIiIkNSIiJDsiIiNLIiQ9IiIkJj4iJHQiIiRBIkYnIiMoKiIkMyJGLEYmRiZGJCIjV0YnIiQsIkYtIiQ0IkYvIiQ5IkYpIiQpPUYtRiZGJyIkLyJGLEYxRixGJSIkLiIiJDYiIiQyIiIjNUY3RjNGJEYlRiZGKSIkaCJGK0YlRixGNiIjWEYvRidGM0YsIiQxIkYlRixGLUY1RiVGNkYpIiRwIkYlRiZGJ0YpRjhGNCIkQCJGLCIkKyJGJUYpRjhGLUY3RjdGLEYnRiZGJEYrRi9GJUYlRjxGNUYtIiMqKkYnRilGO0YoRi8iJDoiRidGJEY/RjZGNUYtRilGOEY/RjVGNkY3RjdGNkYkRjZGL0YmRiciJC0iRi9GLUYsRjZGLEY/RitGJkYsRiZGJkYpRjhGLQ== UVx0TWludH5gdnxed3xodXpgfmFsYXR0aSx+YGVsbWVyfF53fGd2bHRgfmhhcmFuZ29rfCt8K2BoaW50fF53fFx1em5ha2AtZX5gaGFqbmFsb25rfF53fGR1bnRgfmB8Xnd8XHVneWFkbnxed3xcdWxgfCt8K2F+dGl6ZW5ueW9sY35gfF53fGR1dmVzYH5gaXNrb2x8Xnd8XHVzb2tgfCt8K2tpa2V0fmBmZWxha2FzenRhdHR8Xnd8XHVsYDYi
<Text-field style="Heading 1" layout="Heading 1"><Font encoding="UTF-8">6. Sz\303\241mok \303\251s polinomok</Font></Text-field>
<Text-field style="Heading 1" layout="Heading 1"><Font encoding="UTF-8">7. Gyors Fourier-transzform\303\241ci\303\263</Font></Text-field>
<Text-field style="Heading 1" layout="Heading 1"><Font encoding="UTF-8">8. Elliptikus f\303\274ggv\303\251nyek</Font></Text-field>
<Text-field style="Heading 1" layout="Heading 1"><Font encoding="UTF-8">9. Sz\303\241mol\303\241s elliptikus g\303\266rb\303\251ken</Font></Text-field>
<Text-field style="Heading 1" layout="Heading 1"><Font encoding="UTF-8">10. Faktoriz\303\241l\303\241s elliptikus g\303\266rb\303\251kkel</Font></Text-field>
<Text-field style="Heading 1" layout="Heading 1"><Font encoding="UTF-8">11. Pr\303\255mteszt elliptikus g\303\266rb\303\251kkel</Font></Text-field>
<Text-field style="Heading 1" layout="Heading 1"><Font encoding="UTF-8">12. Polinomfaktoriz\303\241l\303\241s</Font></Text-field>
<Text-field style="Heading 1" layout="Heading 1">13. Az AKS teszt</Text-field>
<Text-field style="Heading 1" layout="Heading 1"><Font encoding="UTF-8">14. A szita m\303\263dszerek alapjai</Font></Text-field>
LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn