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 A^2 = B^3 + C^3
 Set {4,b,c,d,e} such that the product of any two of them increased by 1 is a square
 smallest integer whose first n multiples all contain a 3
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 Set {2,b,c,d,e} such that the product of any two of them increased by 1 is a square
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Triangular & Second pentagonal numbers
Suppose the positive integers satisfy ………. (1) Or is a Triangular number [ ] numbers of the form are Second pentagonal numbers. Equation (1) gives us the … Continue reading
Alphametic puzzles — Part 2
(1) are positive integers in arithmetic sequence such that , and Find (2) Substitute each of the letters with a different decimal digit from 0 to 9, to satisfy the following system of simultaneous … Continue reading
Positive integers (a,b,c) in AP; a+b, b+c, c+a are squares
are in arithmetic progression Here are some solutions:
Pythagorean triples (x^2 – 1, y^2 – 1, z^2 – 1)
To find a Pythagorean triangle with sides, where are integers. Here are two examples,
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Concatenation: 2016  x  2016 = y^3
Previous blog: Concatenation: 2016  x  2016 = y^2 Paul found: ……………….. Pipo found: A few more, 2016 appear every 2500 starting at 856 … Continue reading
a^n + b^n + c^n = x^n + y^n + z^n, n = 2, 4
Find six distinct positive integers such that for example, ….. Paul found: … … … … … … … Continue reading
Open question: Positive integers as a sum of squares and cubes?
Every positive integer is a sum of four squares (Lagrange’s Theorem) It is known that every positive integer is a sum of no more than 9 positive cubes, and that every “sufficiently large” integer is a sum of … Continue reading
123456789+987654321
777777 has 48 divisors: 1 3 7 11 13 21 33 37 39 49 77 91 111 143 147 231 259 … Continue reading
Integers that can be written in base n^2 + 1with the same digits but in opposite order
Show that integers of the form and can be written in base with the same digits but in opposite order … Continue reading
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N^5 = A^2 + B^2 for N ≤ 1000
and are nonzero positive integers multiplying both sides by When is the sum of two squares a cube? https://benvitalenum3ers.wordpress.com/2015/05/06/whenisthesumoftwosquaresacube/ multiplying both sides by Solutions when a = 1 … Continue reading