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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.

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## Comments

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TopNewestHint:Induction

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Okay... Can you explain?

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When n=1, the result is 28.Suppose for some n the condition is true.

Multiply by 16^2 and add $15.2^{2n+4}$ and you will get the next such number.So the new number will be congruent to

$256.28+15.2^{2n+4}\equiv 68+15.2^{2n+4}(mod100)$

But $15.2^{2n}$ for odd numbers n will be congruent to 60 modulo 100 (that's not hard to see), so we have proven in inductively.

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