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Olympiad problem - last $3$ digits of $3\times7\times11\times15\times19\times23\times...\times115\times119$

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#elementary-number-theory #contest-math #products #decimal-expansion #arithmetic-progressions
209
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Why isn't $6$ necessarily a divisor of $\ \ \ \cdots 336$?

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#elementary-number-theory #discrete-mathematics #divisibility #decimal-expansion
48
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Three digits are added to a number. Find it.

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#elementary-number-theory #decimal-expansion
419
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In how many zeros does the number 130 choose 70 end?

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#combinatorics #decimal-expansion
1.1k
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Solve an equation system with variables that are raised to decimal power

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#systems-of-equations #decimal-expansion
56
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$x$ is a positive integer with at least 2 digits, a perfect square, and its tens digit is odd. What are the possible units digits of x?

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#decimal-expansion #square-numbers
152
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When is $1234x6789$ divisible by $9$

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#elementary-number-theory #modular-arithmetic #divisibility #decimal-expansion
1.2k
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Sum of digits of $1000^{20}-20$ in decimal notation

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#arithmetic #decimal-expansion
48
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Sum of cubes divisible by $10^6$

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#divisibility #decimal-expansion
1k
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Moving decimal on multiplying or dividing by power of 10

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#fractions #decimal-expansion
166
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Convergence or Divergence of Digital Exponentiation

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#exponentiation #decimal-expansion
65
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$\frac{'ab'}{'ba'}=\frac{'bc'}{'cb'}$

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#algebra-precalculus #proof-writing #decimal-expansion
107
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Prove that the product of the digits of the decimal representation of a natural number never exceeds the number itself.

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#number-theory #elementary-number-theory #contest-math #decimal-expansion
62
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How to determine the original $2$-digit number?

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#number-theory #decimal-expansion #perfect-powers
48
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On $0$'s in repeating decimals.

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#fractions #decimal-expansion

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