Monthly Archives: July 2012

The Last Two Digits of the Square of some Num3ers

Notice the pattern 13^2   =   169                       14^2   =   196 the last two digits of the square of   13   are interchanged, the result is the … Continue reading

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Prime Num3er 41 and its 5-digit multiples

41   is a prime number. Let   abcde   be a multiple of   41,   its digit-rotation numbers: bcdea,   cdeab,   deabc   and   eabcd are also multiples of   41 For example,   41 * … Continue reading

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Fun puzzle: 4-digit Num3er abcd

Find a 4-digit Num3er   abcd   such that (1)   a + b   =   c + d the sum of the first two digits is equal to that of the last two digits. (2)   a + … Continue reading

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a + b + … + n = a * n

Sum of consecutive integers is equal to to the product of the first and the last terms: a, b, c, …, n   are consecutive integers. a + b + … + n = a * n For example, 3 … Continue reading

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Challenging question: Sum of Twin Primes

A twin prime is a prime number that differs from another prime number by two, we write (p, p+2) The first few twin prime pairs are: (3, 5), (5, 7), (11, 13), (17, 19), (29, 31), (41, 43), (59, 61), … Continue reading

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Prime Num3ers Average

The prime numbers under 1000 are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, … Continue reading

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a^4 + b^4

Did you know that a^4 + b^4 = (a^2 + ab 2 + b^2) (a^2 – ab 2 + b^2)       http://en.wikipedia.org/wiki/Factorization     a^4 + 4 b^4 = (a^2 + 2 b^2)^2 – (2ab)^2      

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Sum of 2-digit Numbers is Sum of Squares/Cubes of their digits

(1)   Squares Let ab and cd be 2-digit number, then let’s look for 2-digit number such that (10*a + b) + (10*c + d) = a^2 + b^2 + c^2 + d^2 which gives me   -a^2 + 10*a … Continue reading

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Prime Numbers formed by 2 (or more) consecutive Fibonacci numbers in reverse order

Fibonacci numbers: F(n) = F(n-1) + F(n-2) with F(0) = 0 and F(1) = 1 http://en.wikipedia.org/wiki/Fibonacci_number 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, 17711, 28657, … Continue reading

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Powers that start with 3 & 4 & 5 identical digit

The squares: a(n) = n^2   for n = 0 … 10,000 The cubes: a(n) = n^3   for n = 0 … 10,000 4-th powers: a(n) = n^4   for n = 0 … 1,000 5-th powers: a(n) = … Continue reading

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