Question

Questo NO.
There are two co-prmes such that one number is exactly 8 times the other. What is the sum of the two numbers?
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Answer 1

Answer:

Some examples no-one else has mentioned yet. Since:

n=1+(n−1)

and since 1 is coprime to anything, all numbers n (prime or not) are sums of two coprime integers. For example 1000=1+999. In the other extreme, you can try to write an n as the sum of two almost equal terms. If n is divisible by four, you will do:

4k=(2k−1)+(2k+1)

where 2k−1 and 2k+1 are coprime (can you see why?), for example 1000=499+501. And if n is odd, you do:

2k+1=k+(k+1)

where k and k+1 are coprime, for example with 1001 (not prime) you get 1001=500+501.

Step-by-step explanation: