Let m2 and n2 be a + 22 and a - 23 respectively. ( m > n > 0)

So, we have m2−n2=(a+22)−(a−23)

⇒(m−n)(m+n)=45=1.45=3.15=5.9

⋅

 If m - n =  1 and m + n = 45; then m = 23 ; n = 22; so a=m2−22=n2+23=507

⋅

 If m - n = 3 and m + n = 15; then m = 9 and n = 6, so a = 59.

⋅

 If m - n = 5 and m + n = 9; then m = 7 and n = 2; so a = 27.

Ans : a∈{27;59;507}.

Let m² and n² be a + 22 and a - 23 respectively. ( m > n > 0)

So, we have \(m^2-n^2=\left(a+22\right)-\left(a-23\right)\)

\(\Rightarrow\left(m-n\right)\left(m+n\right)=45=1.45=3.15=5.9\)

\(\cdot\) If m - n =  1 and m + n = 45; then m = 23 ; n = 22; so \(a=m^2-22=n^2+23=507\)

\(\cdot\) If m - n = 3 and m + n = 15; then m = 9 and n = 6, so a = 59.

\(\cdot\) If m - n = 5 and m + n = 9; then m = 7 and n = 2; so a = 27.

Ans : \(a\in\left\{27;59;507\right\}.\)