The three integers are ±13, ±15, and ±17. The difference between ±132 and ±172 is equal to 289 - 169 = 120.
The sum of the squares of two consecutive positive even integers is 340. Find the integers.
The two consecutive negative odd integers having 74 as the sum of their squares are -5 and -7.
The sum of the squares of the three consecutive integers 11, 13, 15 = 515
112+92 is 202.
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12 and 14.
The numbers are 12 and 14.
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:-9 and -88 and 9
42 + 52 = 16 + 25 = 41
Since 16 + 25=41, we know the integers are 4 and 5.
3 and 5
Consecutive square numbers are the squares of consecutive integers. For example, if you take the integers 1, 2, and 3, their squares are 1² = 1, 2² = 4, and 3² = 9, making 1, 4, and 9 consecutive square numbers. These square numbers differ by an increasing odd number: 4 - 1 = 3 and 9 - 4 = 5. Thus, the pattern continues as you square larger consecutive integers.