a^n = a (mod b) for any n> 0

RMLabrador · 2023-03-17, 10:40

for example, for any n>0
$232^{n}\equiv 232 \ (mod \ 319)$

Explain.
Find relations for a and b)

Dr Sardonicus · 2023-03-17, 13:04

Quote:

Originally Posted by RMLabrador

for example, for any n>0
$232^{n}\equiv 232 \ (mod \ 319)$

Explain.
Find relations for a and b)

Hint: We have a^n == a modulo every prime-power factor of b.

wreck · 2023-03-22, 11:30

b|a*(a-1)

2023-03-17, 10:40	#1
RMLabrador "Chereztynnoguzakidai" Oct 2022 Ukraine, near Kyiv. 3D₁₆ Posts	a^n = a (mod b) for any n> 0 for example, for any n>0 $232^{n}\equiv 232 \ (mod \ 319)$ Explain. Find relations for a and b)

2023-03-22, 11:30	#3
wreck "Bo Chen" Oct 2005 Wuhan,China 2×3×31 Posts	b\|a*(a-1)