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could you please help me to solve this these questions tanksScreen Shot</h1><p class='abPRemoveTitle'> 2019-09-23 at 11.45.26 PM.png

Screen Shot 2019-09-23 at 11.45.26 PM.png

1. Let n be a natural number. If the representation in base 3 of n is akak_1 ”410, show
that n is divisible by 9 if and only if a1 = a0 = 0. If the representation in base 10 of n
is brbfil . . . (30, show that n is divisible by 9 if and only if 9 divides b.- + - - - + b0. 2. Let a, b, c be integers such that a2 + b2 = (:2. Prove that at least one of a. and b is even.
If c is divisible by 3, prove that both a and b are divisible by 3. 3. Let a and b be two integers such that gcd(a, b) = 1. Show that gcd(a + b, a — b) = 1 or
gcd(a.+ b,a — b) = 2.

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