RRB NTPC/ASM/CA/TA Exam > RRB NTPC/ASM/CA/TA Questions > (49)15−1is completely divisible by whic...
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(49)15−1 is completely divisible by which number?
(i) 50
(ii) 48
(iii) 29
(iv) 8
(i) 50
(ii) 48
(iii) 29
(iv) 8
- a)ii and iv
- b)iii and iv
- c)i and iii
- d)i and ii
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
(49)15−1is completely divisible by which number?(i) 50(ii) 48(ii...
an−bn is divisible by a−b for all n.
an−bn is divisible by a+b if n is Even.
an+bn is divisible by a+b if n is Odd
(49)15−(1)15, here n = 15 i.e. odd
So it will be divisible by 49−1 = 48
(49)15 can also be written as (72)15 = (7)30
∴ (49)15−(1)15=(7)30−(1)30
So it will also be divisible by 7 + 1 = 8
an−bn is divisible by a+b if n is Even.
an+bn is divisible by a+b if n is Odd
(49)15−(1)15, here n = 15 i.e. odd
So it will be divisible by 49−1 = 48
(49)15 can also be written as (72)15 = (7)30
∴ (49)15−(1)15=(7)30−(1)30
So it will also be divisible by 7 + 1 = 8
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