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1) Use Strong Induction to show that for each n ≥ 1, 10^n may be written...

1) Use Strong Induction to show that for each n ≥ 1, 10^n may be written as the sum of two perfect squares. (A natural number k is a perfect square if k = j 2 for some natural number j. These are the numbers 1, 4, 9, 16, . . . .)

2)Show that if A ⊂ B, A is finite, and B is infinite, then B \ A is infinite. Hint: Suppose B \ A is finite, and obtain a contradiction

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