Q. Find a number x between 0 and 28 with x85 congruent to 6 mod 35.

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Q. Find a number ‘a’ between 0 and 72 with ‘a’ congruent to 9794 mod 73.

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Q. What is the Discrete logarithm to the base 2 (mod 19) for a =7?

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Q. ᶲ(41)=

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Q. ᶲ(27)=

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Q. Find a number ‘a’ between 0 and 9 such that ‘a’ is congruent to 7^1000 mod 10.

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Q. ᶲ(440)=

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Q. GCD(n,n+1) = 1 always.

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Q. ᶲ(231)=

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Q. n is prime if and only if n divides (2n – 2).

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Q. Find x for the CRT when x= 2 mod 3; x= 3 mod 5; x = 2 mod 7

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Q. Consider a function: f(n) = number of elements in the set {a: 0 <= a < n and gcd(a,n) = 1}. What is this function?

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Q. The inverse of 49 mod 37 is –

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Q. Six teachers begin courses on Monday Tuesday Wednesday Thursday Friday and Saturday, respectively, and announce their intentions of lecturing at intervals of 2,3,4,1,6 and 5 days respectively. Sunday lectures are forbidden. When first will all the teachers feel compelled to omit a lecture? Use CRT.

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