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 smallest integer whose first n multiples all contain a 3
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Monthly Archives: November 2014
Pythagorean triples – (a+x)^2 + (b+y)^2 ≤ (c+z)^2
(a, b, c) and (x, y, z) are Pythagorean triples. Prove that Determine when equality holds
Primitive Pythagorean triples – shortest leg is odd
The table shows that all the primitive Pythagorean triples with c ≤ 300, and a is odd. (ca)/2, (c+a)/2, c+b, cb are all perfect squares Prove that if (a, b, … Continue reading
Primitive Pythagorean triples – odd integers
Previous posts: Primitive Pythagorean triples with inradius from 1 to 250 Prove that In all Pythagorean triangles, the inradius is a whole number. The number of primitive Pythagorean triangle with a fixed inradius is always a power of 2. … Continue reading
Num3er 38
38 has 4 divisors: 1 2 19 38 Sum of divisors: 60 38 is a semiprime 38 = 2 * 19 sum of consecutive numbers: 38 = 8 … Continue reading
Primitive Pythagorean triples – polynomials: x^2 + px ± q
If p and q be relatively prime integers, gcd(p,q) = 1 The polynomials are both factorable (over integers) if and only if p and q are respectively the hypotenuse and area of a primitive … Continue reading
All Primitive Pythagorean triples with Palindromic Perimeter < 10^6
Posted in Number Puzzles
Tagged Palindromic Perimeter, Primitive Pythagorean Triples
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(cos x + sin x)/(cos x – sin x) = tan N
Paul found the sequence: 6 * 19, 6 * 49, 6 * 79, 6 * 109,
All Pythagorean triples with Palindromic Perimeter ≤ 89998
All Pythagorean triples with Palindromic Perimeter ≤ 69996
All Pythagorean triples with Palindromic Perimeter ≤ 69996
All Pythagorean triples with Palindromic Perimeter < 49994
a^2 b^2 + b^2 c^2 + c^2 a^2 = d^2
such that a, b, c, d are integers and gcd(a,b,c) = 1 For example, Find more solutions. … Continue reading