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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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Category Archives: Math Beauty
Expression: (x+y+z)(x^5+y^5+z^5) – (x^3+y^3+z^3)^2
Identities : To be continued
Triangle relation
If D is the area of a triangle ABC show that and
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
Square numbers with two different digits
Can you find other examples?
Primitive Pythagorean triples – curious properties
Here are all the primitive Pythagorean triples with c ≤ 300 : In column (1) : the primitive Pythagorean triples In column (2) : the sum of the hypotenuse and one of the legs of a … Continue reading
Num3er of ways of representing any integer N as a sum of 3 distinct positive integers
In how many ways can you express any integer n as a sum of 3 distinct positive integers? that is, where a, b and c are distinct positive integers. For example, There’s only … Continue reading
Repdigit  Legs of Pythagorean triples: 111,222,…,999
Repdigit  Legs of Pythagorean triples : 11, 22, …, 99