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Properties of Multiplication of Integers

show that the...

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show that there is no integer 'a' such that 'a^2-3a-19' is divisible by 289.

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Q. Show that there is no integer a such that

a^{2} - 3 a - 19

is divisible by

289

Q. Find the integer a such that

a^{2} - 3 a - 19

is divisible by

289

.

Q. From a set of 11 square integers, show that one can choose 6 numbers

a^{2}, b^{2}, c^{2}, d^{2}, e^{2}, f^{2}

{(a^{2} + b^{2} + c^{2}) - (d^{2} + e^{2} + f^{2})}

is divisible by

12

9^{n} + 7

is divisible by

8,

where n is a positive integer.

x_{1} = a_{i} b_{i} c_{i}, i = 1, 2, 3

are three-digit positive integers such that each

x_{1}

is a multiple of

19

, then for some integer

n

∣ ∣ ∣ ∣ \begin{matrix} a_{1} & a_{2} & a_{3} b_{1} & b_{2} & b_{3} c_{1} & c_{2} & c_{3} \end{matrix} ∣ ∣ ∣ ∣

is divisible by

19

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