Question 1011506
CONSECUTIVE Integers are n and n+1.
n and n+2 are NOT consecutive integers.
We not know yet if n is odd or is even.  If n odd, then n and n+2 are two consecutive odd integers; and if n is even, then n and n+2 are two consecutive even integers.  What YOU have is not yet clear.


Trying your number and expression,
{{{1/n+1/(n+2)=29/420}}}
Do the algebra and find quadratic {{{29n^2-782n-840=0}}}
and use of general solution for quadratic equation,


{{{n=(782+- 842)/58}}}...... The PLUS form will be {{{highlight(n=28)}}}.


Your two integers, which are NOT consecutive are then  28 and 30.