Tags » Arithmetic Progression

Four consecutive terms of an AP

We know that if you multiply any four consecutive positive integers and add 1 to the product, you’ll get a square number.

The product of four consecutive terms of an arithmetic progression added to the fourth power of the common difference is always a perfect square… 26 more words

Number Puzzles

First Things First

I’m counting to infinity.
I started yesterday at three
And took a break at night to sleep
(But even then I counted sheep
And tallied, too, the several screams… 181 more words


Numbers in A.P. the sum of whose squares is a square

Numbers in arithmetic progressions – common difference d = 3 – the sum of whose squares is a square.

In this puzzle, the sequence needs to have at least 3 terms. 94 more words

Number Puzzles

(x,y,z) in Arithmetic Progression with x^2 – y^2 – z^2 = n

x, y, and z, are consecutive terms of an arithmetic progression,

For n = 27, the equation , has exactly two solutions.

And the equation , has exactly three solutions, for n = … 68 more words

Number Puzzles

A Problem on Number of Divisors

This is a problem I created in . I proposed it to be used here as problem . Though initially I was a bit careless with the bounds, but just to be safe, I am proving the weak bound here. 367 more words

Number Theory

Arithmetic Progression | N = a(a + d1)(a + 2*d1) = b(b + d2)(b + 2*d2)

Find positive integers that can be expressed as the product of three distinct positive integers in A.P. in two ways.

That is,

For example, in one way: … 73 more words

Number Puzzles

Pentagonals (P(2), P(A), P(B)) in arithmetic progression

If , then

c. d. is the common difference

c. d. =

c. d. =

c. d. =

c. d. =

c. d. =

c. d. 37 more words

Number Puzzles