Prove that if a and b are integers, then for any integer k one has (a, b) = (a + kb, b). (Hint: Show that they are mutually divisible.)

The operation:

(a,b) is equal to the rest of the division of a by b.

Now, if we have:

(a + kb,b) = (a,b) + (k*b,b)

But if we have that k and b are integers, then:

(k*b)/b = k

So b divides k*b into a whole number, this means that (k*b,b) = 0

then:

(a + kb,b) = (a,b) + (k*b,b) = (a,b) + 0 = (a,b)

step-by-step explanation:

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3; 9 is 8 to -4

step-by-step explanation: