EM-1626

Number patterns and the nth term

E Math · Secondary 4 · Hard · Number patterns and the nth term

A pattern is formed as follows.

Line 1:

3^2 + 0^2 = (3-0)^2 + 2(3)(0)

Line 2:

5^2 + 1^2 = (5-1)^2 + 2(5)(1)

Line 3:

7^2 + 2^2 = (7-2)^2 + 2(7)(2)

Line 4:

9^2 + 3^2 = (9-3)^2 + 2(9)(3)

Given that

p^2 + q^2

is a line in this pattern with

q < p

and

p^2 + q^2 = 1314

, find the value of

p

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