Question 638986
Not possible.
Adding two odd integers (consecutive or not), you will always get an even number, and 137 is not even.
 
If the sum of two consecutive integers (obviously one of them odd and the other one even) were 137, then we could solve the problem.
We can call two consecutive integers {{{x}}} and {{{x+1}}}
Their sum is {{{x+(x+1)=(x+x)+1=2x+1}}}
If that sum is 137, then
{{{2x+1=137}}} --> {{{2x+1-1=137-1}}} --> {{{2x=136}}} --> {{{2x/2=136/2}}} --> {{{highlight(x=68)}}}