Tags » Arithmetic Progression

(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

Pentagonal numbers in Arithmetic progression

, ,

925 – 330 = 595 = 1520 – 925

, ,

1426 – 590 = 836 = 2262 – 1426

, ,

3015 – 1520 = 1495 = 4510 – 3015…