perplexus.info :: Just Math : Product + Square = Difference of Squares

Product + Square = Difference of Squares (Posted on 2011-07-03)

Three positive integers P, Q and R, with P < Q < R, are in arithmetic sequence satisfying :
N*P*Q*R + Q² = R² - P², where N is a positive integer.

Determine all possible quadruplet(s) (P, Q, R, N) that satisfy the above equation, and prove that no other quadruplet satisfies the given conditions.

Submitted by K Sengupta

Rating: 4.0000 (1 votes)

Solution: (Hide)

There is only a single quadruplet satisfying all the conditions of the problem.
It is given by (P, Q, R, N) = (1, 3, 5, 1).

For a detailed explanation, refer to the solution submitted by Harry in this location.

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
Another approach (Spoiler)	Harry	2011-07-05 19:15:11
Possible solution	broll	2011-07-04 02:08:01

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