Highest Power of a Number

46. A positiv...

Question

46. A positive integer n and has 60 divisiors and 7 n has 80 divisiors the greater integer K such that 7 to the power k divides m is equal to 1) 0 2) 1 3) 2 4) 3

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100

2^{m} 3^{n} 5^{p}

2^{10} {.3}^{8} {.5}^{7}

0 \leq m \leq 10, 0 \leq n \leq 8

0 \leq p \leq 7

(2^{0} + 2^{1} + 2^{2} + . . . + 2^{10}) (3^{0} + 3^{1} + 3^{2} + . . . + 3^{8}) (5^{0} + 5^{1} + 5^{2} + . . . + 5^{7})

2^{10} {.3}^{8} {.5}^{7}

16200

x_{1}, x_{2}, . . . ., x_{n}

^{'} n^{'}

1

n

x_{1} + x_{2} + . . . . + x_{n} = 75

\sum i = 1 \frac{1}{x_{i}}

x_{1}, x_{2}, . . ., x_{k}

^{'} n^{'}

1

n

x_{1} + x_{2} + . . . + x_{k} = 75

\sum i = 1 1 / x_{i}

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