Recall that g is called a primitive root modulo p if the powers of g give all nonzero elements of Fp. (a) For which of the following primes is 2 a primitive root modulo p?a. p = 7b. p = 13c. p = 19d. p = 23

p=13 and p=19.

Step-by-step explanation:

Let <2>={2¹,2²,2³,2⁴,2⁵,2⁶,...} be the set of powers of two modulo p (that is, 2^k=2^kmod p in this set). We can verify if 2 is a primitive root modulo p, by computing (by hand if you like) <2>. If <2> is the set of nonzero elements of Fp, then 2 is a primitive root, if not, then 2 is not a primitive root.

In F_7, <2>={2,4,1}≠F_7\{0}

In F_13, <2>={2,4,8,3,6,12,11,9,2,10,7,1}=F_13\{0}

In F_19, <2>={2,4,8,16,13,7,14,9,18,17,15,11,3,6,12,5,10,1}=F_19\{0}

In F_23, <2>={2,4,8,16,9,18,13,3,6,12,1}≠F_23\{0}

plants store their excess carbohydrate in the form of starch so that it could be used as energy source later on. the excess carbohydrate is converted into starch in the plastid i.e. chloroplast & this process occurs in the presence of sunlight. it is an insoluble polymer of glucose which gets stored in cell organelles named as amyloplasts. in some plants, starch is also stored in roots and embryos.