MathDB

Junior Regional Olympiad - FBH 2015 Grade 6 Problem 4

Source:

10/1/2018

Which number we need to substract from numerator and add to denominator of

\frac{\overline{28a3}}{7276}

such that we get fraction equal to

\frac{2}{7}

FractionDigits

Junior Regional Olympiad - FBH 2015 Grade 7 Problem 4

Source:

10/1/2018

On the market one seller is selling watermelons, melons and young corn cobs. Total number of watermelons, melons and corn cobs is

239

. One buyer bought

\frac{2}{3}

of all watermelons,

\frac{3}{5}

of all melons and

\frac{5}{7}

of all corn cobs. Other buyer bought

\frac{1}{13}

of all watermelons,

\frac{1}{4}

of all melons and

\frac{1}{5}

of all corn cobs. How many pieces in total bought second buyer and how many seller had at the beggining of each watermelons, melons and corn cobs?

number theory

Junior Regional Olympiad - FBH 2015 Grade 8 Problem 4

Source:

10/1/2018

Let

n

be a positive integer and

a=2^n\cdot 7^{n+1}+11

and

b=2^{n+1}\cdot 7^n+3

.

a)

Prove that fraction

\frac{a}{b}

is irreducible

b)

Prove that number

a+b-7

is not a perfect square for any positive integer

n

number theoryIrreducible

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