Question

The product of two positive odd consecutive integers is 4095. What is the larger integer?

Answer 1

Hi,

65

Explanation:

Let's assume 2k-1 the smaller integer, 2k+1 the largest.

`(2k-1)(2k+1)=4095\\\\4k^2-1=4095\\\\4k^2=4096\\\\k^2=1024\\\\k=√(1024) =32\\\\2k+1=2*32+1=\boxed{65}\\\\Proof: 63*65=4095\\`