p.278, icon at Example 6 # 3. (Problem A1 from the 1989 William Lowell Putnam Mathematics Competition.) Consider the sequence of integers (in base 10): 101, 10101, 1010101, 101010101, 10101010101,.... Prove that 101 is the only number in this sequence that is prime. (Hint: Use place value to write each number in terms of the sum of its digits; for example, abcde = a10+ + b10³ + c10² + d10+ e. Then examine how the sum might be factored.)

Module/Week 2 ASSIGNMENT (INPUT/OUTPUT)The number of permutations of a set of n items taken r at a time is given by the following formulan !⁄r !(n-r)!: where n! is the factorial of n, r! is the factorial of r, and (n-r)! is the factorial of the result of n-r. The factorial of a number n can be solved using the following formula: 〖n!=e〗^(-n) n^n√2πn. If there are 18 people in your class and you want to divide the class into programming teams of 3 members, you can compute the number of different teams that can be arranged using this formula (n !⁄r !(n-r)!). Write a C++ program that determines the number of potential team arrangements. You will need to use the double type for this computation. Use the Lab Template you set-up last week, proper formatting, and appropriate comments in your code. The output must be labeled clearly and formatted neatly. Submit C++ Programming Assignment 2 by 11:59 p.m. (ET) on Monday of Module/Week 2.