Question

1. Answer each of the following statements as true, false, or unknown. a. The set of nonnegative even integers is well ordered. b. The sequence of Mersenne numbers forms a geometric progression. c. The sequence {na +1} contains infinitely many primes. d. The sequence {n" +1}.contains infinitely many composites. D) - logo) e. The Prime Number Theorem implies that lim ++00 f. There exist infinitely many pairs of primes that differ by less than 300. g. The number V110520191105201911052019 is rational. h. If ten integers are pairwise relatively prime, then they are mutually relatively prime. i. Let fn and fn+1 be two Fibonacci numbers, where n is a natural number. Then the linear Diophantine equation f3+ n+1 y = 1 has infinitely many integer solutions. j. There are infinitely many regular polygons with an odd number of sides that are con- structible using a straightedge and compass.

Answer 1

a) TRUE

set of non- negative even integers have least element 2

So it is well ordered.

b) False

Mersenne numbers are of the form 2ⁿ -1 , n € N

It is not a geometric series as we have no common ratio between successive terms.

C)TRUE

the sequence {n⁴+1}  contains INFINITELY many primes for even values of n. i.e. for n=2,4,6...

d) TRUE

the same sequence {n​⁴+1} contains INFINITELY many composites for odd values of n. i.e. for n= 1,3,5,....

You can verify this for many values by putting those values for n.

Plz upload the rest bits in another question.