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 A^2 = B^3 + C^3
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 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: May 2013
Making 24 with the days of the Month : June, 2013
Today is May 31, 2013, that is, 2013531, try to make 24 of (20, 13, 5, 31) One possible answer: ceiling(√31) + floor(√13) + … Continue reading
2digit Num3ers  DigitSum and DigitProduct
Let ab be a 2digit number DigitSum (ab) = a + b DigitProduct (ab) = a * b N = 10*a + b – (a … Continue reading
Sums and products of pairs of num3ers are squares
a + b = x^2 a * b = y^2 Here are the first few examples 2^2 = 2 + 2 2^2 = 2 * 2 … Continue reading
5digit num3ers divisible by 3digit contained in the middle of the num3ers
11371 11371 / 137 = 83 11398 … Continue reading
Concatenation  x^4 * y = x  4  y
Older post: Concatenation  x^2 * y = x  2  y x^4 * y = x  4  y Here are few solutions: 3^4 … Continue reading
2digit num3ers expressible as 10*a + b – (a^2 + b^2)
To find a 2digit number ab such that ab – (a^2 + b^2) = N, N = 10, 11, 12, 13 … , 99 10 … Continue reading
Concatenation  x^2 * y = x  2  y
x^2 * y = x  y x^2 * y = x  2  y For example, 3^2 * 375 = 3375 … Continue reading
x^2 + k = y^3
x^2 + k = y^3 If k = 0 Trivial cases: x = y = 0 and x = y = 1 8^2 = 64 = … Continue reading
Numbers whose fifth power is the sum of 5th powers
12^5 = 11^5 + 9^5 + 7^5 + 6^5 + 5^5 + 4^5 Can you find other 5th powers that can be expressed as the … Continue reading
Concatenation  (x + y)^2 = x  y
To find integers N such that N = (x + y)^2 = x  y N = (x – y)^2 = x  y For example, 364^2 = … Continue reading