Question 65
We will say that a positive integer $n$ is subject to an *interesting* change if it is multiplied by $2$ and the result is increased by $4$, a *special* change if it is multiplied by $3$ and the result is increased by $9$ and an *awesome* change if it is multiplied by $4$ and the result is increased by $16$.
a) Show that there exists a positive integer which after three changes, the first – interesting, the second – special and the third – awesome, becomes $2020$.
b) Find all positive integers with the property that after two changes of different types, selected among the three above, becomes $2014$.
a) Show that there exists a positive integer which after three changes, the first – interesting, the second – special and the third – awesome, becomes $2020$.
b) Find all positive integers with the property that after two changes of different types, selected among the three above, becomes $2014$.