Wednesday, 13 January 2016

modular arithmetic - Prove that $53^{53}-33^3$ is divisible by $10$

Prove that $53^{53}-33^3$ is divisible by $10$



I don't know modular arithmetic, so I tried things like that:



$53^3 \cdot 53^{50}-33^3=(33+20)^3 \cdot 53^{50}-33^3=(33+20)(33+20)(33+20)\cdot 53^{50}-33^3$
but I get stuck and don't know how to continue

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