Suppose that you want to calculate 1434661 · 3785648743 − 100020304 · 54300201. You are told that the answer is a positive integer less than 90. Compute the answer mod 10 and mod 9, then combine to get the answer. Show all the necessary work to obtain your answers. Note: This technique has often been employed to do calculations with large integers because most of the computations use small integers, with only the Chinese Remainder Theorem step requiring large integers. For example, if the answer is known to be less than 1036, the calculations can be done mod p for each prime less than 100. Since the product of the primes less than 100 is approximately 2.3 × 1036, the Chinese Remainder Theorem gives the answer exactly

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Problems on numbers

Number theory is one of the most appealing topics in mathematics. Given one or more numeric values, a numeric algorithm performs some computation. The use of number theory in computing is important for applications like in the case of cryptographic algorithms. Number theory is also used in various applications such as calculating hash functions or in information security. Euclid’s algorithm is one of the oldest number-theoretic algorithms which is used to calculate the greatest common divisor of two numbers.