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This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.

When posting on Brilliant:

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## Comments

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TopNewestyes it must have i;e solve by indicies a+b=2

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The bases are not same. Additionally, there's no multiplication involved so you cannot add the indices.

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$c^2 \equiv 0, 1, 4, 9, 6, 5 \pmod{10}$

$5^a \equiv 5 \pmod{10}$

$8^b \equiv 8, 2 \pmod{10} (b \text{ is odd})$

$5^a + 8^b \equiv 3,7 \pmod{10}$

Clearly, the first statement and the last statement share no residues. Thus proven.

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What's mod? And how are 6 and 5 also included?

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$a \equiv b \pmod c$

Implies a leaves same remainder as b when divided by c.

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Haha, the same way I solved the question!

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Nice problem. By the way , from where have you collected these problems?

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