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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
 Set {3,b,c,d,e} such that the product of any two of them increased by 1 is a square
 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: November 2012
Num3er 1588
Marin Mersenne (8 September 1588 – 1 September 1648) The factors of 1588 are: 1 2 4 397 794 1588 The prime factors are: 2 * 2 * … Continue reading
Num3ers that are divisible by 2digit numbers contained in them
For example, 132 132 / 12 = 11 135 135 / 15 = 9 612 612 / 12 = 51 and many others. They are not very interesting since they are only divisible by one 2digit number … Continue reading
Sum of even positive squares
2^2 + 4^2 = 4*5 2^2 + 4^2 + 6^2 + 8^2 + 10^2 = 4*5 + 5*6 + 6*7 + 7*8 + 8*9 we see that in these two cases that the sum of even positive squares … Continue reading
Repeating decimal 0.19 and 0.199
0.19 stands for the repeating decimal (= 19/99): 0.1919191919191919191919191919191919191919191919191919… and 0.199 for (= 199/999) 0.1991991991991991991991991991991991991991991991991991… 0.19 + 0.199 = 19/99 + 199/999 = 391118/999999 that is, … Continue reading
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Concatenation puzzle: when (A  B) / B is an integer
Concatenation is the joining of two numbers by their numerals. That is, the concatenation of 444 and 777 is 444777. Concatenation of numbers A and B is denoted A  … Continue reading
Can You Crack Pigeon’s Secret Wartime Code?
LONDON (Reuters) – A World War Two code found strapped to the leg of a dead pigeon stuck in a chimney for the last 70 years may never be broken, a British intelligence agency said on Friday. Watch the Reuters … Continue reading
Num3er 1170
Leonardo Pisano Fibonacci 1170 – 1250 The factors of 1170 are: 1 2 3 5 6 9 10 13 15 18 26 30 … Continue reading
Num3er 1913
Paul Erdős 1913 – 1996 The year in which mathematician Paul Erdős was born is an emirp. 1913 is the smallest prime p such that its next prime (1931) is an anagram of p An emirp (“prime” … Continue reading
Pythagorean triple – Digits Reversed
Pythagorean triple – Definition: A Pythagorean triple consists of three positive integers a, b, and c, such that a^2 + b^2 = c^2 (33, 56, 65) is one example of a primitive Pythagorean triangle in which the … Continue reading
Num3er 75
The factors of 75 are: 1 3 5 15 25 75 The prime factors are: 3 * 5 * 5 75 is 1001011 in base 2 2210 … Continue reading