Every us coin is stamped with the year in which it was


Question: 1. Prove, or find a counterexample: the difference of two consecutive perfect squares is odd.

2. Every US coin is stamped with the year in which it was minted. How many coins do you need to have in your pocket to be assured that at least two of them have the same last digit? How many do you need to be assured that at least two have the same first digit?

3. Prove, or find a counterexample: the sum of two perfect squares is even.

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Mathematics: Every us coin is stamped with the year in which it was
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