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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: October 2012
Happy Halloween! Time for Vampire Num3ers (including a puzzle)
Definition: http://mathworld.wolfram.com/VampireNumber.html A number v = x * y with an even number of digits formed by multiplying a pair of n/2digit numbers (where the digits are taken from the original number in any order) x … Continue reading
Num3er 36
The factors of 36 are: 1 2 3 4 6 9 12 18 36 The prime factors are: 2 * 2 * 3 * 3 36 … Continue reading
Num3er 159
The factors of 159 are: 1 3 53 159 The prime factors are: 3 * 53 Using each of 9 digits 19 once: 159 * 48 = 7632 … Continue reading
Num3er 100001
Goal: To find positive integers a, b, c, d, e so that 1^2 + a^2 + b^2 = c^2 + d^2 + e^2, and 1 … Continue reading
In how many ways x + y + z = 1000
In how many ways can you make sums of three distinct positive integers total (a) 24 (b) 25 (c) 1000 For example, 1 + 2 + 21 = 24, 1 + 2 + 997 = 1000, … Continue reading
Patterns: Num3ers of the form 1001, 110011, …
My focus: To examine numbers of the form, 1001, 110011, 11100111, 1111001111, … and to replace the middle two digits (00) with the prime numbers 11 and 13 For example: (1) 1001 = 7 * … Continue reading
Num3er 10001
Goal: To find positive integers a, b, c, d, e so that 1^2 + a^2 + b^2 = c^2 + d^2 + e^2, (sum of three … Continue reading
Num3er 1001
Goal: To find positive integers a, b, c, d, e so that 1^2 + a^2 + b^2 = 1001 = c^2 + d^2 + e^2, … Continue reading
Pairs (a,b); a^2 + a*b + b^2 = c^2
If (a, b) are two positive integers, we know that, a^2 + 2 ab + b^2 is a perfect square. [ a^2 + 2 ab + b^2 = (a + b)^2 ] Goal: To … Continue reading
Palindromic prime 313
313 is a palindromic prime (Palprime). Palindromic primes: prime numbers whose decimal expansion is a palindrome: 2, 3, 5, 7, 11, 101, 131, 151, 181, 191, 313, 353, 373, 383, 727, 757, 787, 797, 919, 929, 10301, 10501, 10601, … Continue reading
Posted in Math Beauty, Number Puzzles
Tagged 313, Beautiful Number, Palindromic primes, Prime Numbers
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