A number exactly between 60 and 70 decreased by 9 times 6 added to 2 multiplied by a number is 241.2 what is the number
Answers
Answer:
What are the two numbers lying between 60 and 70, each of which exactly divides 2^43-1?
None, because the smallest prime factor of the number in question is 431. However, I can demonstrate how this question could have been solved without calculators, had it been correct.
If a number n divides 243−1 then we have that 243≡1 mod n . This rules out all the even n in the range [60,70] since the remainder of an even number after division with another even number must be even.
The remaining candidates for n are 61, 63, 65, 67 and 69. We can easily rule out 61 and 67 from this list because they are primes and for an odd prime p , we know that 2k≡1 mod p if and only if k≡0 mod (p−1) . In our case 43 is not divisible by either 60 or 66.
Now, 243 can be re-written as 2×647 . For n=63 , we get 2×647 mod 63=2 .
By process of elimination, the answer should have been 65 and 69 but it is not since your question is incorrect.
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Happy MakarSankranti (◔‿◔)
