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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,

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

Adding up congruences, we get

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

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