`p` is a prime number and `n

Is 1 a prime number ?

Write each of the following sentences in symbolic form using statement variables p and q. (i) 19 is not a prime number and all the angles of a triangle are equal. (ii) 19 is a prime number or all the angles of a triangle are not equal. (iii) 19 is a prime number and all the angles of a triangle are equal. (iv) 19 is not a prime number.

Let a ,b in na n a > 1. Also p is a prime number. If a x^2+b x+c=p for any intergral values of x , then prove that a+b x+c!=2p for any integral value of xdot

lf r, s, t are prime numbers and p, q are the positive integers such that their LCM of p,q is r^2 t^4 s^2, then the numbers of ordered pair of (p, q) is (A) 252 (B) 254 (C) 225 (D) 224

sqrtp (where p is a prime number) is

The function f(x)=(4sin^2x−1)^n (x^2−x+1),n in N , has a local minimum at x=pi/6 . Then (a) n is any even number (b) n is an odd number (c) n is odd prime number (d) n is any natural number

If N is a prime number which divides S=^(39)P_(19)+^(38)P_(19)+^(37)P_(19)+…+"^(20)P_(19) , then the largest possible value of N among following is

Consider p to q : If today is Sunday their 3 is a prime number Her p: Today's Sunday, q:3 is a prime number. The truth of p to q is T because the conculsion of has truth value T. Consequences.

Statement 1: If p is a prime number (p!=2), then [(2+sqrt(5))^p]-2^(p+1) is always divisible by p(w h e r e[dot] denotes the greatest integer function). Statement 2: if n prime, then ^n C_1,^n C_2,^n C_2 ,^n C_(n-1) must be divisible by ndot