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Addition of Integers

If a, b, c ar...

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If a, b, c are positive integers such that abc+ab+ac+bc+a+b+c=1000 then a+b+c=?

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a, b, c, x

are positive integers, then

∣ ∣ ∣ ∣ ∣ \begin{matrix} a^{2} + x & a b & a c a b & b^{2} + x & b c a c & b c & c^{2} + x \end{matrix} ∣ ∣ ∣ ∣ ∣

is divisible by

Q. If a, b, c and x are positive integers, then

∣ ∣ ∣ ∣ ∣ \begin{matrix} a^{2} + x^{2} & a b & a c a b & b^{2} + x^{2} & b c a c & b c & c^{2} + x^{2} \end{matrix} ∣ ∣ ∣ ∣ ∣

is divisible by

Q. If a + b + c +ab +bc + ca + abc = 2005 where a, b, c are distinct natural number such that a < b < c then

Q. Find number of triplets

(a, b, c)

possible such that

(a^{b})^{c} = 4

a, b, c

are positive integers only.

If a,b,c are unequal and positive ,show that bc/(b+c ) +ac/(c+a) +ab/(a+b) is less than1/2(a+b+c)

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