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Determine the smallest positive integer such that 60^n+k*71^n is divisible by 1441 for all odd positive integers n

 Jul 18, 2019
 #1
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+2

Does this problem let usage of a calculator? Because I used a calculator to discover that the factors of 1441 are 131 and 11.

 

*To check if a number is prime

 

So knowing that 131 and 11 multiply to 1441, we can see that miraculously if you substitute 1 for n in your equation 60+ k * 71n you get 131*k. And since 11 multiplied by 131 is 1441, k should be \(\boxed{11}\).

 Jul 18, 2019
edited by CalculatorUser  Jul 18, 2019
edited by CalculatorUser  Jul 18, 2019
edited by CalculatorUser  Jul 18, 2019
 #2
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+1

I think that only works for where n=1, but it says it must work for all odd integers, sorry D:, also I think 60+71*k doesnt equal 131k

Also, yes, calculators are allowed.

Guest Jul 19, 2019
 #3
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The smallest n =1 and all ODD number thereafter, 3, 5, 7, 9........etc.

The value of  k = 263

 Jul 19, 2019
 #4
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+1

thank you it was right

so how do i mark a question as done on this website

Guest Jul 19, 2019
 #5
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+1

That is done by the Moderators, CPhill, Melody, Alan.....etc. 

 Jul 19, 2019

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