Question 299888
{{{N(N+1)=272}}}
{{{N^2+N-272=0}}}
Look for integer factors close to {{{sqrt(272)=16.49}}}
{{{16*17=272}}}
{{{(N-16)(N+17)=272}}}
Since we only want positive solutions,
{{{N-16=0}}}
{{{N=16}}}
16 and 17 are the two consecutive positive integers whose product is 272.