$a^{11762}\equiv a^2\pmod {25725}$ ; the smallest a where in this congruence is false?
Question From Brilliant.org, and I am having trouble understanding the top voted solution (I dont think anyone would answer if i commented on a 3 year old question)
User Otto Bretscher said that:
"If 7 divides $a$ with multiplicity 1 then $a^{11762}\equiv 0 \ne a^2\pmod{343}$"
Can someone elaborate on this please, why did it say congruent to 0 but not to $a^2$?