文摘
In this paper we show that at most class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0012365X15002915&_mathId=si1.gif&_user=111111111&_pii=S0012365X15002915&_rdoc=1&_issn=0012365X&md5=a31f33745657a85c2f79b83db19a2b12" title="Click to view the MathML source">2gcd(m,n)class="mathContainer hidden">class="mathCode"> points can be placed with no three in a line on an class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0012365X15002915&_mathId=si2.gif&_user=111111111&_pii=S0012365X15002915&_rdoc=1&_issn=0012365X&md5=34c56b7bbed0c700c69e116b8d22a5e9" title="Click to view the MathML source">m×nclass="mathContainer hidden">class="mathCode"> discrete torus. In the situation when class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0012365X15002915&_mathId=si3.gif&_user=111111111&_pii=S0012365X15002915&_rdoc=1&_issn=0012365X&md5=3514d55c7fe2cd782f90a25c4ad2861f" title="Click to view the MathML source">gcd(m,n)class="mathContainer hidden">class="mathCode"> is a prime, we completely solve the problem.