What Is the Fundamental Theorem of Arithmetic?
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- FundamentalFundamentalFundamental TheoremTheoremTheorem ofofof Arithmetic!Arithmetic!Arithmetic! The Fundamental Theorem of Arithmetic states that every positive integer has a u…
By Evan Tong, Victor Wang
- Fundamental Theorem of Arithmetic Let's look at one of the most interesting theorems of high school math. Recall that a prime number is a number ppp that only has 2 positive div…
By Ananya Kumar, Victor Wang
- A prime factorization of a natural number n >>> 1 expresses n as a product of powers of distinct primes. n=∏i=1kpilin = \prod_{i = 1}^{k}p_i^{l_i}n=i=1∏kpili Examples: 60=2⋅3…
By Vinitha Ranganeni
Problems 3
- If 201120112012=xx2011^{2011^{2012}} = x^x201120112012=xx for some positive integer xxx, how many positive integer factors does xxx have? Source: 2011-2012 Winter Online Math Open
- The number 96+19^6+196+1 is the product of 333 primes. Find the largest prime.
- For which integers n>1n > 1n>1 is (n−1)!(n-1)!(n−1)! divisible by nnn?