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Higher Study | Mathematics | Elementary Number Theory

If a ≡ b mod(n) and b ≡ c mod(n) , then
Necessary condition to apply the Chinese remainder theorem is modulo of congruence should be:
For any integers a and b, and positive integer n, choose the incorrect statement:
If p is a prime then for any integer a 
If a and b are any positive integers and a ≡ b(mod n) then 
If p is prime then,ϕ (p!) is equal to 
If m and n are positive integers with m and n are relatively prime then, mϕ (n) + nϕ (m) is congruent to
The linear congruence ax ≡ b(mod n) has a solution if and only if,
Consider a linear congruence a ≡ b (mod m), Choose the false relation from the option given below:
Choose the false statement:
For any positive integers 'p' and 9, there exist unique integers 'a' and 'b' such that p = 9a + b, where b must satisfy:
For any positive integers 'a' and 3, there exist unique integers 'q' and 'r' such that a = 3q + r, where r must satisfy:
Deep has 825 red candies and Maya has 675 green candies. They want to arrange the candies in such a way that each row contains equal number of candies and also each row should have only red candies or green candies. What is the greatest number of candies that can be arranged in each row?
What is the value of ϕ (1001)?
Which of the following relations defines the Euclid's Division Lemma:
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