Saturday, December 28, 2019

elementary number theory - Solving a Linear Congruence




I've been trying to solve the following linear congruence with not much success:
19 congruent to 1921x(mod26)



If anyone could point me to the solution I'd be grateful, thanks in advance


Answer



Hint: 26=213 and the Chinese remainder theorem. Modulo 2 we have to solve 1x(mod2), that is x=2k+1 for some k, now solve 1942k+21(mod13).


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