Tags » Arithmetic Progression

a^2 - 1, b^2 - 1, c^2 - 1 in arithmetical progression



We want , , to be in arithmetical progression

and the sum to be a square number


Here are the first few solutions:

(14, 26, 34) 38 more words

Number Puzzles

Integers (a,b,c) whose squares form an A.P. --- Part 2

In part 1, I started a discussion on the ordered triples of integers whose squares form an arithmetic progression.

In other words,
, or equivalently… 113 more words

Number Puzzles

Integers (a,b,c) whose squares form an arithmetic progression --- Part 1



Let’s look at ordered triples of integers whose squares form an arithmetic progression.

In other words,
, or equivalently

The solutions are of the form… 66 more words

Number Puzzles

Integers(a,b,c,d) in A.P. whose number of divisors is also in A.P.


229, 361, 493, and 625 are in arithmetic progression:

361 – 229 = 493 – 361 = 625 – 493 = 132

and the number of divisors of each is also in arithmetic progression: 84 more words

Number Puzzles

A^3 + B^3 + C^3 + D^3 = N^2, (A,B,C,D) in A.P.



A, B, C, and D form an arithmetic progression.
Let d be the common difference.


d = 1 ……..
d = 14 …… … 145 more words

Number Puzzles

Special triplets of 4-digit Prime numbers




1487, 4817, and 8147 are prime numbers such that

>> Each of 4817 and 8147 is obtained by permuting the digits of 1487, and… 118 more words

Prime Numbers