Question

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prove that h.c.f (a-b,a+b) = 1 or 2, if h.c.f (a,b) = 1.

Please solve this question with and explain it.

Answer 1

As Hcf of a and b is 1 hence both of them can’t be even hence there are two possibilities 1 is even and 1 is odd and both of them are odd
Now when when add or subtract and odd and an even number u always get an odd number hence first condition is ki that the hcf is 1
Now when both of them are odd
Now when u have two odd numbers when u subtract or add u get even numbers which when divided by each other they only have one 2 in common