If N = 7^2014 Then: A) The Last Digit is 7 B) Rem

Question

If N = 7^2014 Then:A) The Last Digit is 7B) Remainder upon division by 24 is 1C) Remainder upon division by 25 is 1D) No. Of digits in N > 1700

Aditya Gupta · Accepted Answer

N= 7^(2*1007)= (7^2)^(1007)= 49^1007= (48+1)^1007= 48k + 1 (using binomial theorem, k is an integer).= 24(2k)+1= 24q + 1hence, the remainder is 1 when divided by 24.for remainder by 25, write 49= 50 – 1= 25(2) – 1,and you ll find N= 25q – 1= 25(q – 1) + 24, hence remainder is 24 not 1.for last digit, we simply need to find remainder on division by 10, write 49= 50 – 1= 10*5 – 1 and then proceed.KINDLY APPROVE :))

Algebra> If N = 7^2014 Then: A) The Last Digit is ...

If N = 7^2014 Then:
A) The Last Digit is 7
B) Remainder upon division by 24 is 1
C) Remainder upon division by 25 is 1
D) No. Of digits in N > 1700

Shadic The Hedgehog , 5 Years ago

Aditya Gupta

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Algebra> If N = 7^2014 Then: A) The Last Digit is ...

If N = 7^2014 Then:A) The Last Digit is 7B) Remainder upon division by 24 is 1C) Remainder upon division by 25 is 1D) No. Of digits in N > 1700

Shadic The Hedgehog , 5 Years ago

Aditya Gupta

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If N = 7^2014 Then:
A) The Last Digit is 7
B) Remainder upon division by 24 is 1
C) Remainder upon division by 25 is 1
D) No. Of digits in N > 1700