Question

the number of integers satisfying the condition g.c.d (a,b)=5 anda+b=100 is​

Answer 1

the number of integers satisfying the condition g.c.d=100

Answer 2

Given:

Consider the given condition

g.c.d(a, b) = 5 and a + b = 100

Find:

We have to find number of integers that satisfy the condition

Solution:

Since we have given gcd (a, b) = 5

this implies there exists integer k such that b = 5k+a

also we have given that a + b = 100

now substitute the value of b into this equation

a + 5k + a = 100

5k + 2a = 100

This shows that there is many values of k satisfy and hence there exists infinitely many values which satisfy the given condition.