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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: September 2013
Prime Num3ers p; DigitSum (p) = DigitSum (p^2)
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, … Continue reading
Prime numbers P such that P ± DigitProduct(P) is prime
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, … Continue reading
Num3ers of the form 10*x + y = (x^3 + y^3)/(x + y)
x^3 + y^3 ——————— = 10*x + y x + y x^3 + y^3 ——————— = 100*x + y x + y (3^3 + 7^3) / … Continue reading
Number 17328
The record for most Girl Scout cookie boxes sold by a single girl is 17328, set by Jennifer Sharpe at age 15. Mich. girl scout sells 17,328 boxes of cookies —————————————— 17328 has 30 divisors: 1 … Continue reading
Arithmetic Sequence  cube roots
In an Arithmetic Sequence the difference between one term and the next is a constant. If a, b, c form an arithmetic sequence, we can write a, b = a + d, c … Continue reading
Some musings on π — Part 4
3.141592653589793238462643383279502884197169399375105820974944592307816406286 Let’s form palindromes from the reflected pi digits and see how many primes we can produce: 3 is a prime number. 313 is a prime number. 31413 = 3 * 37 * 283 … Continue reading
N/k is equal to the sum of the squares of digits of N
Solving the two equations (10*x + y)/k = x^2 + y^2 (100*x + 10*y + z)/k = x^2 + y^2 + z^2 for … Continue reading
Num3er 513
513 is the concatenation of primes 5 and 13 513 = 5  13 513 has 8 divisors: 1, 3, 9, 19, 27, 57, 171, 513 Sum of … Continue reading
Num3er 3079
According to “The QI Elves” @qikipedia, 3079 chemical compounds have been identified in human pee so far. 3079 is the 440th prime number. 3079 = 5^5 – (1^2 + 3^2 … Continue reading
Puzzle  4 positive numbers
a, b, c, d are four positive numbers – not necessarily integers. There are six ways to multiply pairs of them: a*b, a*c, a*d, b*c, b*d and c*d. We … Continue reading