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number theory

for any prime p , prove that exist an infinty of integers n , such that ,p|2^n - n

Note by Med Fatnassi
3 years, 3 months ago

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by fermat's thm, p|2^[p-1] -1 ........(1) choose n=k(p-1) so, p|2^k[p-1] -1 (obtained from 1 by factorizing) p|2^n - n reduces to p|k+1 so infinite +ve integers k can be found

Sayak Chakrabarti - 2 years, 2 months ago

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