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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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Monthly Archives: February 2015
Num3er 729243027001
is a 12digit perfect cube. with a digit sum of 37: and it can be sectioned in powers of 3 : since Is a number with such properties unique? Paul found: … Continue reading
Triangle  Trig questions
Consider the triangle shown below with angles A, B, and C. Suppose that the length of the side opposite angle A has length a, the side opposite angle B has length b, and the side opposite angle C has … Continue reading
Squares that can be transformed into a cube if two digits are increased by one
excluding , , etc. excluding , etc Contributor: pipo
Squares that can be transformed into a cube if one digit is increased by 1
Paul found: 39204 = 198^2 39304 = 34^3 39204000000 = 198000^2 39304000000 = 3400^3 98831640625 = 314375^2 98931640625 = 4625^3 pipo found: 1199462890625 … Continue reading
Are there any positive integers n such that the expansion of 2^n ends in n?
n = 36 is the first from this list. Any others? @chappulian found n = 736 and n = 8736 @shahlock: n = 48736 Dave Radcliffe: a(2) = 36, … Continue reading
Squares that can be transformed into another square if some digits are increased by 1
Here are a few examples, 8digit square that can be transformed into another square if the 2nd digit from the left is increased by 1. 38564100 = 39564100 = 24502500 = 25502500 … Continue reading
Determinant  (A,B,C) are the angles in a triangle
If A, B, C are the angles of a triangle show that