Four type of numbers

Number Theory Level 2

$\bigcirc + \bigcirc + \bigcirc = \text{Abundant number}$

$\bigcirc - \bigcirc - \bigcirc = \text{Rational number}$

$\bigcirc \times \bigcirc \times \bigcirc = \text{Fibonacci number}$

$\bigcirc \div \bigcirc \div \bigcirc = \text{Perfect number}$

Only 1-9 distinct digits are allowed to use in every four cases. Can we make all four equations true?

No Yes

1 solution

Munem Shahriar
Oct 17, 2017

$2 + 7 + 3 = 12 \longrightarrow \text{Abundant number}$

$10- 1 -4 = 5 \longrightarrow \text{Rational number }$

$2 \times 4 \times 1 =8 \longrightarrow \text{Fibonacci number}$

Now considering the last equation.

$\bigcirc \div \bigcirc \div \bigcirc = \text{Perfect number}$

Between 1 and 9, 6 is the only perfect number. It is impossible to get 6 in this case.

Hence the answer is $\color{#20A900} \boxed{\text{no}}$