INTRODUCTION. Noticethat l .23.4?+ = 52, 2 2.3.4 5 +I = 112, 3.4. 5 6 + 1 = 192 . Indeed, it is well known that the product of any four consecutive integers ...

INTRODUCTION. Notice that 1 · 2 · 3 · 4 + 1 = 52, 2 · 3 · 4 · 5 + 1 = 112, 3 · 4 ·. 5 · 6 + 1 = 192,.... Indeed, it is well known that the product of any ...

A result that lends itself to investigation by secondary students is the propo- sition that the product of four consecutive positive integers is never square.

Oct 4, 2020 · The product of five consecutive integers is indeed a perfect square of an integer. Plainly, at least one of them is neither divisible by 2 2 nor 3 3.

In this note we prove the conjecture for I = 2 and all k; that is, we prove that a product of consecutive integers is never a square. The method is similar ...

Duration: 8:47
Posted: Feb 8, 2024

Squares in products from a block of consecutive integers by. R. Balasubramanian (Madras) and T. N. Shorey (Bombay). 1. Let k ≥ t ≥ 2, m ≥ 0, y ≥ 1 be ...

Dec 12, 2020 · Letting the three integers be x-1, x and x+1, note that (x-1)(x+1) and x are coprimes. So, if (x^2–1)x is a square, then x must be a square as must

Duration: 7:02
Posted: Nov 2, 2023