The difference between the squares of two consecutive integers j and j+1 is |2j+1|. There are therefore two such pairs where this quantity is 17:
Bob
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8
15 and 16
12 and 13 (and you may note that 12+13 = 25)
24 and 25, which are (49-1)/2 and (49+1)/2
There are two consecutive even numbers. The numbers are 62 and 64.
8
15 and 16
62 and 63
12 and 13
12 and 13 (and you may note that 12+13 = 25)
The numbers are 13 and 14.
24 and 25, which are (49-1)/2 and (49+1)/2
17 and 18
The numbers are 12 and 14.
The numbers are 12 and 14.
Let's call n the first one the problem is (n+1)2-n2=17 = 2n+1 then n = 8
Consecutive numbers are whole numbers whose difference is 1.