Find positive integers n and a1 a2an such that a1a2an 1000

Find positive integers n and a1, a2,........,an such that a1+a2+........+an = 1000 and the product divisable by 7?

Solution

Since the product is divisible by 7 so one of the integer must be divisible by 7

So choose 7 and rest be any other integers whose sum will be 1000

so 7+193+8+192+9+191+10+190+11+189

sum of all these is 1000

And also the product is divisible by 7

nuner of terms ,n = 10