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Number Theory

# Modular Arithmetic Operations: Level 1 Challenges

What is the last digit when

$1234 \times 5678$

is multiplied out?

If today is a Monday, then what day will it be 100 days later?

$\LARGE \color{red} 5^{\color{blue}8^{\color{green}{12}^{\color{purple}{15}^{\color{brown}{104}}}}} + \color{red}1$

Determine the smallest prime divisor of the gigantic number above.

One of the seven goblets above is made of real gold. If you start counting at A and wind back and forth while counting (A, B, C, D, E, F, G, F, E, D, ...), then the golden goblet would be the $$1000^\text{th}$$ one that you count.

Which one is the golden goblet?

If $$a$$ is a negative odd number and $$b$$ is a positive even number, then which of the following must be a positive even number?

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