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1. (Integers: primes, divisibility, parity.) (a) Let n be a positive integer. Prove that two numbers na +3n+6 and n2 + 2n +7
2. (Integers: %, =) (a) Suppose a, b, n are integer numbers and n > 0. Prove that (a+b)%n = (a%n +B%n)%n. (b) Let a, b, n be
4. Rational, irrationals (a) Prove that log3 (27) - 5 is irrational. (b) Let r and y be two positive integer numbers. Prove t
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Answer #1

(6 Let n = 1526 152 78 63 6986567767. So, n has last digit = 7 Then, u has last digit=9. 1:7772427 Similarly na has last digiAt 13 last, to check if Harl) % 6 attends all the values and 5. het m=2 , then 4a+1=8m-3=13 and (hati)%6=13%6=1, if m=3 then

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