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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: June 2014
Puzzle  quadruplet (1, 22, 41, 58)
Consider the quadruplet (a, b, c, d) = (1, 22, 41, 58) the sum of any three of them is a perfect square: 1 + 22 + 41 = 64 1 + 22 + 58 … Continue reading
Powers of 2 puzzle
Let M be a positive integer. Rearranging the digits of M, we obtain the positive integer N. No leading zeros. Is it possible to have two different positive integer powers of 2 this way? … Continue reading
Puzzle  Solve a + b + c + d = n √(abcd) (positive integers)
I like this number 1281: Concatenation of 3*4  3^4, DigitSum(1281) = 12. First two digits: 12 1+2+8+1 = 3√(1*2*8*1)
Puzzle  Factoring the Difference of Two Squares
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Heronian triangle Area = k*(Perimeter), k is a prime number
The lenghts of the sides of an isosceles triangle are integers, and its area is the product of the perimeter and a prime. What are the possible values of the prime? Answer: 2, 3, 5 … Continue reading
Puzzle  8digit Num3ers
How many 8digit numbers are there in which every digit occurs the same number of times as the value of the digit? e.g. 3414434, digit 1 occurs 1 time, digit 3, 3 times, … Continue reading
Integer N such that N = DigitSum (N^n), n = 3,4,…,10
Determine the smallest integer N with N = DigitSum (N^n), n > 10 For example, Here’s a large one: 2015^137, DigitSum(2015^137) = 2015 Any others? … Continue reading
When N – DigitSum(N) and N + DigitProduct(N) are both squares
Republic of Math @republicofmath says: in base 3 : 2 , 7 , 1457 in base 9 : 2, 8, 24, 73, 80, 161, 265, 1313, 2719, 38446 … Continue reading