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Big Powers

Note by Llewellyn Sterling
1 year, 11 months ago

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We can easily prove that $$3^{444}+4^{333}$$ is divisible by $$5$$ using Modular Congruences.

Observe that

$3^{444} \equiv 9^{222} \equiv (-1)^{222} \equiv 1 {\pmod 5}$

Similarly,

$4^{333} \equiv (-1)^{333} \equiv -1 {\pmod 5}$

$3^{444}+4^{333} \equiv 1 + (-1) \equiv 0 {\pmod 5} \quad _\square$ · 1 year, 11 months ago