2024年4月3日发(作者：逄念寒)

The7

th

RomanianMasterofMathematicsCompetition

SolutionsfortheDay1

ereexistaninfinitesequenceofpositiveintegersa

1

,a

2

,a

3

,...suchthat

a

m

anda

n

arecoprimeifandonlyif|m−n|=1?

(Peru)JorgeTipe

werisintheaffirmative.

Theideaistoconsiderasequenceofpairwisedistinctprimesp

1

,p

2

,p

3

,...,coverthe

positiveintegersbyasequenceoffinitenon-emptysetsI

n

suchthatI

m

andI

n

aredisjointifand

2024年4月3日发(作者：逄念寒)

The7

th

RomanianMasterofMathematicsCompetition

SolutionsfortheDay1

ereexistaninfinitesequenceofpositiveintegersa

1

,a

2

,a

3

,...suchthat

a

m

anda

n

arecoprimeifandonlyif|m−n|=1?

(Peru)JorgeTipe

werisintheaffirmative.

Theideaistoconsiderasequenceofpairwisedistinctprimesp

1

,p

2

,p

3

,...,coverthe

positiveintegersbyasequenceoffinitenon-emptysetsI

n

suchthatI

m

andI

n

aredisjointifand