Primes lurking nearby

Number Theory Level 3

$\large \color{#302B94}x \color{#20A900}y+\color{#302B94}x+\color{#20A900} y=\color{#3D99F6}{96}$

How many solutions are there such that both $x$ and $y$ are positive integers satisfying the equation above?

1 2 4 0 3

1 solution

Tijmen Veltman
Apr 9, 2015

Adding one we obtain $(x+1)(y+1)=97$ , which is prime. Hence either one of the factors must be equal to 1 at most, making either $x$ or $y$ equal to 0 or less. Therefore the number of solutions with $x$ and $y$ positive integers is $\boxed{0}$ .

Moderator note:

Simple and elegant. Nice!

That's great, exactly how it should be done

Eamon Gupta - 6 years, 2 months ago

Great work sir .upvoted.

Rohit Udaiwal - 5 years, 9 months ago

Primes lurking nearby

1 solution

Moderator note:

0 pending reports