Show that any integer of the form 5n can be written as

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Question :

Suppose that nickels and pennies disappear from the currency system and we have only dimes and quarters. Obviously any product that costs 15 cents can not be exactly paid for using only dimes and quarters.

Show the following using induction: For every n greaterthanorequalto 4, any product that costs 5n cents can be paid for exactly using only dimes and quarters".

Equivalently, show that any integer of the form 5n (n ≥ 4) can be written as 10x + 25y for some non-negative integers x and y.

Reference no: EM132142070

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