Question

10. Let p + 2,5 and suppose there exists a number a such that p divides a' - 5. Show that p = 1 or 4 mod 5

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Could you please solve this problem with the clear hands writing to read it PLEASE? Also the good explanation to understand the solution is

the subject is Number theory

Answer 1

It is given that p# 2,5 and PLA 5. It is clear that ^ = 5 (mod p). That means is the quadratic Deguide.modulo... that is. ........... Since 53d (mod 4), quad datie Tecipaceity Shows that this is equivalent to f .. > This memoram that premamaneh se Mbretit From 0, @ I = f. By the Verifying that quendantic Desidues. module, this is one if...PE 004 mod 5.