If nis an odd natural number, prove ged(n. n + 2) = 1 and express 1...

  

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If nis an odd natural number, prove ged(n. n + 2) = 1 and express 1 as a linear combination of the two numbers. If a and b are relatively prime natural numbers, prove ged(ab, a² + b² ) = 1 (use the key fact about primes). Find all the distinct solutions to the linear congruence 33z 36mod105 (show steps don't just give the answer). (This one is EXTRA CREDIT) Suppose a and b are natural numbers such that ged(a, b) 1. Prove that god(a+b. a-b)= 1 or 2 (HINT: First show if d = ged(a + b. a - b),then explain why d | 2a and d | 2b). = If nis an odd natural number, prove ged(n. n + 2) = 1 and express 1 as a linear combination of the two numbers. If a and b are relatively prime natural numbers, prove ged(ab, a² + b² ) = 1 (use the key fact about primes). Find all the distinct solutions to the linear congruence 33z 36mod105 (show steps don't just give the answer). (This one is EXTRA CREDIT) Suppose a and b are natural numbers such that ged(a, b) 1. Prove that god(a+b. a-b)= 1 or 2 (HINT: First show if d = ged(a + b. a - b),then explain why d | 2a and d | 2b). =