Prove that any integer a ge 7 is the of two relatively prime integers- -We say two integers m and n are relatively prime their HCF -i-e- GCD- is 1-

Question

Toppr Admin · Accepted Answer

Let a be any integer-When a is odd then a-p-q where either p is even or q is even-If p is even then q is odd and hence p and q are relatively prime to each other-xA0-Similarly- vice versa-Therefore- GCD-p-q-1Hence- any integer-xA0-n-x2265-7 is the sum of two relatively prime integers-

Prove that any integer a≥7 is the sum of two relatively prime integers. (We say two integers m and n are relatively prime if their HCF (i.e., GCD) is 1)

Let a be any integer.When a is odd then a=p+q where either p is even or q is even.If p is even then q is odd and hence p and q are relatively prime to each other. Similarly, vice versa.Therefore, GCD(p,q)=1Hence, any integer n≥7 is the sum of two relatively prime integers.

Prove that any integer $a \geq 7$ is the sum of two relatively prime integers. (We say two integers $m$ and $n$ are relatively prime if their HCF (i.e., GCD) is $1$ )