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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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Monthly Archives: October 2013
Prime factorization of Num3ers from 4 to 1000
4 = 2 * 2 6 = 2 * 3 8 = 2 * 2 * 2 9 = 3 * 3 10 = 2 * 5 12 = 2 * 2 * 3 14 = 2 * 7 15 … Continue reading
Concatenation Num3ers ABCDE such that ABCDE = 45*A*B*C*D*E
5digit number: A, B, C, D, E are all 1digit numbers. 77175 = 45 * 7 * 7 * 1 * 7 … Continue reading
System of equations  (x + y)^n = z, n= 3,5
To find all possible triplets (x, y, z) of real numbers with x ≤ y ≤ z that (1) (x + y)^3 = z (y + z)^3 = x (z … Continue reading
Composite Num3ers and their Prime factors w/ same digits
Number 1255 Property: the number and its prime factors have the same digits: 1255 = 5 * 251 12955 = 5 * 2591 1299955 = 5 * 259991 … Continue reading
Integers under 1000 expressible as a sum of four integer cubes
All integers n ≤ 350 can be expressed as a sum of four cubes for example, 2 = (22)^3 + 4^3 + (41)^3 + 43^3 30 = 4^3 + (5)^3 … Continue reading
Num3er 1024
October 24 can be expressed as 10/24 or 1024 = 2^10 1024 = 32^2 … It is the smallest 4digit square number 1024 is an even square: … Continue reading
DigitReversal(N), DigitSum(N)  Squares of 1202, 2012, 2021, 2022, 2102, 2202
The squares of : 1202, 2012, 2021, 2022, 2102, 2202 1202^2 = 1444804 … Continue reading
Puzzle  (x + y + z)^k – (x^k + y^k + z^k)
(x + y + z)^2 – (x^2 + y^2 + z^2) = 2(xy + xz + yz) (x + y + z)^3 – (x^3 + y^3 + z^3) = 3(x + y) (x + z) (y … Continue reading
DigitReversal(N), DigitSum(N)  Squares of 1212, 12112, 121112, …
1212^2 = 1468944 4498641 = 2121^2 … Continue reading
DigitReversal(N), DigitSum(N)  Squares of 1122, 11222, 112222, …
1122^2 = 1258884 4888521 … Continue reading