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?

Chung Kevin by Chung Kevin

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

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Chung Kevin by Chung Kevin

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.

Martin Soliman by Martin Soliman

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?

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Psalm Lemuel Guevarra by Psalm Lemuel Guevarra

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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Anuj Shikarkhane by Anuj Shikarkhane
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