Show that there are an infinite number of primes of the form 4k + 1 and of the form 4k+ 3.

The number of divisors of the form 4K + 2 , K ge 0 of the integers 240 is

(2)/(3)x-(1)/(4)y=6 kx-(1)/(3)y=8 If the system of equations above has an infinite number of solutions, what is the value of the constant k?

Show that any positive odd integer is of the form 4q+1 or 4q+3 , where q is some integer.

Show that any positive odd integer is of the form 4q+1 or 4q+3 , where q is some integer.

Show that any positive odd integer is of the form 4q+1 or 4q+3 , where q is some integer.

Three non-zero real numbers form a AP and the squares of these numbers taken in same order form a GP. If the possible common ratios are (3pm sqrt(k)) where k in N , then the value of [(k)/(8)-(8)/(k)] is (where [] denotes the greatest integer function).

Express in the form of complex number (1-i)^4

The total number of divisors of the number N=2^(5).3^(4).5^(10).7^(6) that are of the form 4K+2, AAK in N is equal to

If the value of the sum n^(2) + n - sum_(k = 1)^(n) (2k^(3)+ 8k^(2) + 6k - 1)/(k^(2) + 4k + 3) as n tends to infinity can be expressed in the form (p)/(q) find the least value of (p + q) where p, q in N

Find the value of k so that 8k +4, 6k-2, and 2k + 7 will form an A.P.