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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 2014
Puzzle  Almost Repdigit – Divisibility
Can you find (a, b) such that each of the “almost” 6digit numbers abbbbb, babbbb, bbabbb, bbbabb, bbbbab and bbbbba is divisible by the same 1digit number and baaaaa, abaaaa, … Continue reading
Sets of primitive pythagorean triples with perimeter almost equal
(a, b, c) is a Pythagorean and primitive with a perimeter p (x, y, z) is a Pythagorean and primitive with perimeter p + 2 Find two triples and … Continue reading
Heron triangle such that the Area is a square number
Find more examples
Pythagorean triples – Perimeter is a perfect square
Here are some examples Find more examples.
Puzzle  Two rectangles
Area of rectangle #1 = 3 * Area of rectangle #2 Perimeter of rectangle #2 = 3 * Perimeter of rectangle #1 Here are some solutions: … Continue reading
A^n + A^m contain all digits from 0 to 9
To find integer A such that contain all digits from 0 to 9 For example Find other examples.
Puzzle  Two 2digit semiprimes
Find two 2digit numbers (A, B) such that A, B, (AB) are all semiprimes, where the 6 primes used are all different. And A + B is a square E.g. … Continue reading
Pythagorean triples – shortest leg is prime
All the prime numbers less than 1000: 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, … Continue reading
Expressing integers using only digit 1
Let F(N) be the minimum of digit 1 to represent N and using the operations (+, *) (1) ……………… ……………… (2) Show that (3) Representing prime numbers Is it true for a prime … Continue reading
Square numbers with two different digits
Can you find other examples?