Number System II

Monday 20 February 2012

Representing a number as prime factors helps in analyzing problems.

$N = p^a + q^b + r^c$ Where p, q, r are prime numbers and a, b, c are the number of times each prime number occurs.

Number of Factors = (a + 1)(b + 1)(c + 1)

${{(a+1)(b+1)(c+1)} \over 2}$
Sum of Factors = ${({a^{p+1} - 1})({b^{q+1} - 1})({c^{r+1} - 1}) \over {(a-1)(b-1)(c-1)}}$

Concept of cyclicity is used to find unit's digit in case the numbers are occuring in powers.

Cyclicity of 1, 5, 6 - 1

Cyclicity of 4, 9 - 2

Cyclicity of 2, 3, 7, 8 - 4

${n \over p} + {n \over p^2} + {n \over p^3} + \dots$ Next

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