Tag Archives: Arithmetic Progression

Three numbers in A.P. whose sum is a 6-th power

      Find three numbers in arithmetical progression whose sum is a 6-th power.                                             Advertisements

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Triangle(a,b,c); a^2, b^2, c^2 and cot of interior angles are in A.P.

  Let     be the sides of triangle such that     are in A.P. Prove that the cotangent of the interior angles are also in A.P.                         … Continue reading

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To make {(a+b-c), (a+c-b), (b+c-a)} all squares, (a,b,c) in AP

    Find three numbers     in arithmetic progression such that (1)    (2)    (3)      ,     ,     where the common difference is   (1)      ………..   (2)      ………..   (3) … Continue reading

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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) (322, 362, 398) (4898, 5042, … Continue reading

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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 The solutions are of the form for any integers     … Continue reading

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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 for any integers     and   The ordered triple … Continue reading

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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   =   … Continue reading

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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 ……   d = 22 …… … Continue reading

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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 >>    … Continue reading

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Oblong numbers : x(x+ 1), y(y+ 1), z(z+ 1) in arithmetic progression

  An Oblong number is a number which is the product of two consecutive integers, that is, a number of the form       There exist infinitely many triplets of positive integers   ,   for which the numbers … Continue reading

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