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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: Multiples
ndigit number multiple of 2^n, written with 6s’ and 7s’
Find the lowest ndigit number multiple of , written only with 6s’ and 7s’ The first few examples, n = 1 … … 6 n = 2 … Continue reading
Multiples of 37 and their permutations
A 6digit number in which the first 3 digits are consecutivelyincreasing numbers; and the last 3 digits, consecutivelydecreasing numbers, is divisible by 37. For example, Can you explain why? —————————————— (1) If a 3digit number of … Continue reading
Moving one digit from one end to the other of a number
(period 6) Move 7 : (period 6) Move 4 : (period 6) Move 1 : (period 6) Move 8 : (period 6) Move 5 : (period 6) Move 2 : (period … Continue reading
Pattern  Sum of all positive integers (multiples of 2 and 5 excluded)
multiples of 2 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, … multiples of 5 5, 10, 15, 20, 25, 30, … Let’s take the sum of all positive integers which … Continue reading
Smallest multiples of N ending in N with sum of digits N (11 ≤ N ≤ 99)
11 ≤ N ≤ 99 To find the smallest multiples of N that ends in N and the sum of digits is N For example, here are the smallest multiples of 13, 17, 19 that satisfy … Continue reading
N/k is equal to the sum of the squares of digits of N
Solving the two equations (10*x + y)/k = x^2 + y^2 (100*x + 10*y + z)/k = x^2 + y^2 + z^2 for … Continue reading
A ddigit num3er multiple of 2^d
For example, d = 76 2^76 = 75557863725914323419136 A 76digit number that is a multiple of 2^76 containing only the digits 6 and 7 is: 6667776766677767667676666776766667777767666677766776777777777777666766667776 = 2^76 * 88247290723637794367680048552939376696792027490086866 … Continue reading
Multiple of 2^d of ddigits containing digits of 2^d
For example, 2^2 = 4 A multiple of 2digit containing only 4 is 44 2^3 = 8 A multiple of 3digit containing only 8 is 888 2^5 = 32 A multiple of … Continue reading
Multiples of 3digit num3ers containing one of its digits
Goal: To find 3digit numbers such that its consecutive multiples contain one of its digits For example, the number 471 471 * 1 = 471 471 * 2 = … Continue reading
5digit num3ers divisible by 3digit contained in the middle of the num3ers
11371 11371 / 137 = 83 11398 … Continue reading