2. APRN In homework problem 17 in section 3.1 you showed that there are an infinitenumber of primes whose decimal form ends with a 1. For every other digit 2-9 decide whetherare an infinite number of primes ending in that digit or a finite number of primes ending in thatdigit. Prove your result.

We will use basic knowledge of number theory to answer this question.

Answered: APRL In homework problem 17 in section…

Advanced Engineering Mathematics

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Chapter2: Second-order Linear Odes

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Fibonacci's Rabbits Leonardo Fibonacci da Pisa (c. 1170-1250), an outstanding European mathematician of the middle ages stated an interesting problem in his main work Liber Abaci (1202) where he wanted to know how many pairs of rabbits will be produced in a year, beginning with a single pair, if in every month each pair brings forth a new pair that becomes productive from the second month on and assuming no pairs die. Therefore, starting with F1 = 1 newly born pair in the first month, we can find the number Fk of pairs in the kth month. Using some knowledge of calculus, acquired when studying sequences, we can determine the number of pairs of rabbits in the kth month by setting up the following equation: Fk = (Number of pairs alive the preceding month) + (Number of newly born pairs for the kth month) Since the rabbits do not produce offsprings during the first month of their lives, we can see that the number of newly born pairs for the kth month is the number Fk - 2 of pairs alive…
4. Given the first four primes, for how many distinct pairs is the product odd? (A) 1 (B) 2 (C) 3 (D) 4 (E) 5
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ERCISES 5.1.7. Solve the following problems. 1) Find the number of 5-lists of the form (21, 22, 23, 24, 25), where each , is a nonnegative integer and x₁ + x₂ + x3 + x4 + 3x5 = 12. 2) We will buy 3 pies (not necessarily all different) from a store that sells 4 kinds of pie. different ord possible? List all of the possibilities (using A for apple
a)Select a variety of one- and two digit numbers between 1 and 99 and multiply by 9. Record your results. b) Find the sum of the digits in each of your products in part (a). If the sum is not a one digit number find the sum of the digits of the resulting sum again until you obtain a one -digit number, c) make a conjecture about the sum of digits when a one- or two digit number is multiplied by 9

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APRL In homework problem 17 in section 3.1 you showed that there are an infinite number of primes whose decimal form ends with a 1. For every other digit 2-9 decide whether are an infinite number of primes ending in that digit or a finite number of primes ending in that digit. Prove your result.