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Q: What are the 2 consecutive positive even numbers the sum of whose squares is 340?

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The numbers are 12 and 14.

122 + 142 = 340

8

The numbers are 13 and 14.

15 and 16

17 and 18

62 and 63

12 and 13

The numbers are 8 and 9.

12 and 13 (and you may note that 12+13 = 25)

6,7,8 those numbers squared are 36,49,64 which add to 149

Consecutive numbers are whole numbers whose difference is 1.

There are two consecutive even numbers. The numbers are 62 and 64.

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

Any pair of consecutive numbers will have an odd total. 10 and 12 are consecutive even numbers that total 22.

24 and 25, which are (49-1)/2 and (49+1)/2

The numbers are 20 and 21.

The numbers are 244 and 245.

The numbers are -8, and -7.

The numbers are 64 and 65.

There is no set of four consecutive whole numbers whose sum is 75.

They are perfect squares.

There is no set of 3 consecutive odd numbers whose product is 6,873. However, there is a set of 3 consecutive odd numbers whose sum is 6,873: 2289, 2291, and 2293.

8,9,10,11,12

There is no set of 8 consecutive whole numbers whose sum is 75.