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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: December 2013
Puzzle  Num3er 2014
Older post: Puzzle  Num3ers 2013 and 2014 2014 has 8 divisors: 1 2 19 38 53 106 1007 2014 Sum of divisors: 3240 2013, … Continue reading
Puzzle: X in base 8 and Y in base 9
X is a 4digit number in base 8 Y is a 4digit number in base 9 such as Y base9 – X base8 = 1 DigitSum(Y) – DigitSum(X) = 1 Find X and Y For example, 3056 … Continue reading
Num3er 371
Tweet: 371 years ago today, the great Isaac Newton was born via @CoolR1a @grahamfarmelo Newton, Sir Isaac (1642–1727) —————————————— 371 has 4 divisors: 1 7 53 371 Sum of divisors: … Continue reading
Puzzle Sequence of repdigits: as simple as 1,2,3
1 (1+2+1) = 2^2 (1+2+3+2+1) = 3^2 (1+2+3+4+3+2+1) = 4^2 (1+2+3+4+5+4+3+2+1) = 5^2 (1+2+3+4+5+6+5+4+3+2+1) = 6^2 (1+2+3+4+5+6+7+6+5+4+3+2+1) = 7^2 (1+2+3+4+5+6+7+8+7+6+5+4+3+2+1) = 8^2 (1+2+3+4+5+6+7+8+9+8+7+6+5+4+3+2+1) = 9^2 121 = 11^2 121*(1+2+1) = 22^2 121*(1+2+3+2+1) = 33^2 121*(1+2+3+4+3+2+1) = 44^2 121*(1+2+3+4+5+4+3+2+1) = … Continue reading
Integers such that N^5 = A^5 + B^5 + C^5 + D^5 + E^5
(1) A^5 = B^5 + C^5 + D^5 + E^5 + F^5 For example, 72^5 = 67^5 + 47^5 … Continue reading
Puzzle Factorial of digits of prime numbers (under 1000)
2digit primes : ab is a 2digit prime. Conditions : Let’s find primes such that: ab > a! * b! ab – (a! * b!) ab + (a! * b!) ab * a! * b! – 1 … Continue reading
Puzzle  Num3ers 2013 and 2014
Find smallest integers (x, y) so that 2013*x is square, 2014*x a cube, and 2013*y is a cube, 2014*y a square
4digit number abcd = (k+a)(k+b)(k+c)(k+d)
abcd = (k + a)(k + b)(k + c)(k + d) abcd is a 4digit number and k is a positive integer. For example, k = 5 1500 = (5 + 1)(5 + 5)(5 + 0)(5 + … Continue reading
Posted in Math Beauty, Number Puzzles
Tagged 3digit Numbers, 4digit Num3ers, digital product, DigitProduct, Factors
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2digit numbers whose cube can be expressed as the sum of cubes
6^3 = 3^3 + 4^3 + 5^3 12^3 = 6^3 + 8^3 + 10^3 = 3^3 + 4^3 + 5^3 + 8^3 + 10^3 13^3 = 5^3 + 7^3 + 9^3 + 10^3 = 1^3 + 5^3 + 6^3 … Continue reading