let `f(x)=a_0+a_1x^2+a_2x^4+............a_nx^(2n)` where `0< a_0 < a_1 < a_3 ............< a_n` then `f(x)` has

Let f(x) = a_0+a_1x+a_2x^2+........a_nx^n , where a_i are non-negative integers for i = 0, 1, 2..........n . If f(1) = 21 and f(25) = 78357 . Then, find the value of f(10) .

Let p(x) = a_0+a_1x+ a_2x^2+.............+a_n x^n be a non zero polynomial with integer coefficient . if p( sqrt(2) + sqrt(3) + sqrt(6) )=0 , the smallest possible value of n . is

If (1+x+x^2)^n = a_0+a_1x+a_2x_2 +..............+a_(2n)x^(2n) then the value of a_1+a_4+a_7+.........

If (1+x+x^2)^n=a_0+a_1x+a_2x^2+.......+a_(2n)x^(2n) , then prove that a_0+a_2+a_4+....+a_(2n)=1/2(3^n+1) .

If (1-x+x^2)^n=a_0+a_1x+a_2x^2+ .........+a_(2n)x^(2n),\ find the value of a_0+a_2+a_4+........+a_(2n)dot