If a,b,c are positive integers, then find the number of solutions of the equation

∑a + ∑ab = 4198 - abc, where ∑ denotes summation of terms, one at a time and two at a time respectively.

Pls provide solution with explanation

these are good questions which u should not ask for the solution of. try urself no matter how much time it takes.

Hi Speed Racer.

See here that,

a+b+c+ab+bc+ca = 4198 - abc

Now, (a+1)(b+1)(c+1) = a+b+c+ab+bc+ca+abc+1.

So the above equation can be written as (a+1)(b+1)(c+1) = 4199.

Now factorise 4199... 4199 = 13*17*19.

So the triplet is (12,16,18)

Which can be arranged in 3! ways for a,b,c.

Hence 6 Solutions.

Best Regards,

Ashwin (IIT Madras).