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Natural Numbers

THE SUM OF AL...

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THE SUM OF ALL NATURAL NUMBERS 'N' SUCH THAT 1001 IS A) 3203 B

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Q. Call a natural number

n

faithful, if there exist numbers

a < b < c

a

b, b

c

n = a + b + c

. Show that all but a finite number of natural numbers are faithful. Find the sum of all natural numbers which are not faithful.

Q. The sum of all natural numbers

^{'} n^{'}

100 < n < 200

(91, n) > 1

A = [\begin{matrix} 2 & - 1 \\ 3 & - 2 \end{matrix}], then A^{n} =

A = [\begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix}]

, if n is an even natural number

(b)

A = [\begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix}]

, if n is an odd natural number

(c)

A = [\begin{matrix} - 1 & 0 \\ 0 & 1 \end{matrix}], if n \in N

(d) none of these

Q. Find all pairs of consecutive odd natural numbers, both of which are larger than

10

, such that their sum is less than

40

Q. The sum of all natural numbers

^{'} n^{'}

100 < n < 200

(91, n) > 1

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