2017/008) Let P be a polynomial such that $P(x)=a_0+a_1x+?+a_nx^n$where $a_0,a_1,\cdots$? are non-negative integer. Given that P(1)=4 and P(5)=152 find P(6)

P(x) is a cubic polynomial as P(5) is 152 between $125(5^3)$ and $625(5^4)$
now coefficient of $x^3$ is 1
so $P(x) = x^3 + ax^2 + bx + c$
taking mod 5 we get c =2 so $P(X) = x^3 + ax^2+ bx + 2$ and so $a . 5^2 + 5b = 152-125-2 = 27$ giving a = 1, b= 2
sp $P(x) = x^3 +x ^2 + 2$ and it satisfies P(1) = 4
so P(6) = 254