Number Theory

Modular Arithmetic Operations

Modular Arithmetic Operations: Level 1 Challenges


What is the last digit when

1234×5678 1234 \times 5678

is multiplied out?

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

581215104+1 \LARGE \color{#D61F06} 5^{\color{#3D99F6}8^{\color{#20A900}{12}^{\color{#69047E}{15}^{\color{#624F41}{104}}}}} + \color{#D61F06}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 1000th1000^\text{th} one that you count.

Which one is the golden goblet?

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


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