Question

If the product of four consecutive natural numbers increased by a natural number p is a perfect square then find the value of p​

Answer 1

Answer:

We need the value of "p" which will make {n(n+1)(n+2)(n+3)+p} a perfect square. Now we know that since n is a natural number, n^2+3n will be a natural number and hence a will be a natural number as well. Therefore the product now is in the form a^2 + 2a clearly (1) short of a perfect square.

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