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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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Tag Archives: Powers of 2
Powers of 2 and 3 as a sum of two powers
and so on. and so on. and so on.
Triples (a, b, c); abc, bca, cab are all powers of 2
Find triples of positive integers for which and are all powers of 2 For example, (a, b, c) = (2, 2, 2), (3, 2, 2), (11, 6, 2), … Continue reading
Powers of 2  (2+1)(2^2 + 1)(2^4 + 1)(2^8 + 1) … + 1
Using powers of 2: 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, … as shown we always end up getting 4. Explain. … Continue reading
Find smallest integer n so that 2^(10*n) doesn’t begin with digit 1
These results all begin with 1 : Find the smallest positive integer where produces a number that does not begin with 1 —————————————— Solution: Don S. McDonald and … Continue reading
Powers of 2 – divisibility
Let be positive integers. and …. …… …. …… …. …… … ….. … ….. … Continue reading
Powers of 2 in terms of factorials
Generalize this.
Are there any positive integers n such that the expansion of 2^n ends in n?
n = 36 is the first from this list. Any others? @chappulian found n = 736 and n = 8736 @shahlock: n = 48736 Dave Radcliffe: a(2) = 36, … Continue reading
2^(4*n+2) + 1, n = 1,2,3,…,15
To be continued.
Powers of 2 puzzle
Let M be a positive integer. Rearranging the digits of M, we obtain the positive integer N. No leading zeros. Is it possible to have two different positive integer powers of 2 this way? … Continue reading