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Monthly Archives: January 2015
Num3ers such xyz + x(10y + z) + (10x + y)z = 100x + 10y + z
for example, 155 Find a 4digit number abcd such that a*b*c*d + abc*d + ab*cd + a*bcd = abcd Pipo found : 6550 = 6*5*5*0 + … Continue reading
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Find sequence of integers: DigitProduct(N)/DigitSum(N)
Consider 3489 the product of its digits divided by the sum of its digits (3*4*8*9)/(3+4+8+9) = 36 is an integer Repeat the process: (3*6)/(3+6) = 2 Stop the process when you end up with a 1digit … Continue reading
Numbers (< 1000) such that concatenation of their prime factors is a prime number
Part 1 Each concatenation is composed by two different digits:
Patterns with 1/13
(period 6) (period 6) (period 6) (period 6) (period 6) (period 6) (period 6) (period 6) (period 6) (period 6) (period 6) (period 6) … Continue reading
Patterns with 1/7
(period 6) Move 7 : (period 6) Move 4 : (period 6) Move 1 : (period 6) Move 8 : (period 6) Move 5 : (period 6) … Continue reading
Equations: A^2 + B^3 = C^4 and D^3 + E^4 = F^5
Find positive integer solutions to (1) (2) For example, (1) is a prime number. —————————————— (2) … Continue reading
Products  (x + r_1)(y + r_2) = xy; (r_1, r_2) are rational
Example #1 : , Integer solutions: , ……………………………………………….. Example #2 : , Integer solutions: , ……………………………………………….. Integer solutions: , ……………………………………………….. there are infinitely many possibilities. … 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
(10*a + b) * c = a^2 + b^2 + c^2
Paul found – Part 1 Pattern #2 :