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 smallest integer whose first n multiples all contain a 3
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Monthly Archives: December 2014
Squared 10tuples (a,b,c,d,e,f,g,h,i,j)
Older post: Squared 9tuples (a,b,c,d,e,f,g,h,i) To find 10tuples such that are square numbers. 9tuples : (3, 4, 12, 84, 204, 1428, 3468, 24276, 58956) gcd(3, 4, 12, 84, 204, 1428, 3468, 24276, … Continue reading
Concatenation Sum of consecutive integers: a+b+…+n = an
Find other solutions Manan Shah found: David found: 203 + 202 + … + 28 = 20328 = 203  28 217 + … Continue reading
Pythagorean triples with hypotenuse = 333,3333,…
To find recurrence relations (whenever possible) with the following triples: Here’s, for example, a recurrence relation for (660, 3267, 3333)
Pythagorean Triangle – lesser known formula
(a, b, c) is a Pythagorean triple shortest leg = a longest leg = b Let the perimeter be and the area. since and Hence, … Continue reading
N basea = DigitReversal(N) baseb
475 decimal = 733 base8 = 337 base12 1337 decimal = 935 base12 = 539 base16 —————————————— some examples where the … Continue reading
Squared 9tuples (a,b,c,d,e,f,g,h,i)
To find 9tuples such that are square numbers. Here are the first few examples: (3, 4, 12, 84, 204, 1428, 3468, 24276, 58956) gcd(3, 4, 12, 84, 204, 1428, 3468, 24276, 58956) = 1 (3, … Continue reading
Squared 8tuples (a,b,c,d,e,f,g,h) and gcd(a,b,c,d,e,f,g,h) = 1
To find 8tuples such that are square numbers. Here are the first few examples: (3, 4, 12, 84, 204, 1428, 3468, 24276) gcd(3, 4, 12, 84, 204, 1428, 3468, 24276) = 1 (3, 4, … Continue reading
Squared 7tuples (a,b,c,d,e,f,g) and gcd(a,b,c,d,e,f,g) = 1
To find 7tuples such that are square numbers. Here are the first few examples: (3, 4, 12, 84, 204, 1428, 3468) gcd(3, 4, 12, 84, 204, 1428, 3468) = 1 (3, 4, 12, 84, … Continue reading
Squared 6tuples (a,b,c,d,e,f) and gcd(a,b,c,d,e,f) = 1
To find 6tuples such that are square numbers. Here are the first few examples: (3, 4, 12, 84, 204, 1428) gcd(3, 4, 12, 84, 204, 1428) = 1 (3, 4, 12, 84, 204, … Continue reading
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Squared 5tuples (a,b,c,d,e), gcd(a,b,c,d,e) = 1
To find 5tuples (a, b, c, d, e) such that a < b < c < d < e gcd (a, b, c, d, e) = … Continue reading