primes
<br /="/"/><div>Any prime>3 can be written as 2n-1 or 2n+1 where n is an integer. Can it also written as mn-1 or mn+1, where m=3,4,5,6? (prove is needed for each m). If the answer is true, what is the smallest even m such that the question is not true and what is the smallest odd m such that the question is not true? Thanks.</div><span style="display:none;">www.ddhw.com</span><br /="/"/><br /="/"/> <div style="MARGIN-TOP:20px;MARGIN-LEFT:0;MARGIN-BOTTOM:0;float:left"></div>回复：primes
<table cellpadding="8" height="100%" width="100%"><tr><td valign="top"><br /="/"/><div>Sorry, They should be 5 and 8 respectively.</div><span style="display:none;">www.ddhw.com</span><br /="/"/><br /="/"/> <div style="MARGIN-TOP:20px;MARGIN-LEFT:0;MARGIN-BOTTOM:0;float:left"></div></td></tr></table>Thanks. You are right.
<table cellpadding="8" height="100%" width="100%"><tr><td valign="top"><br /="/"/><div>Using these forms, it is easy to prove that the sum of twin primes can be divided by 12 when the primes are bigger than 3. </div><span style="display:none;">www.ddhw.com</span><br /="/"/><br /="/"/> <div style="MARGIN-TOP:20px;MARGIN-LEFT:0;MARGIN-BOTTOM:0;float:left"></div></td></tr></table>回复：Thanks. You are right.
<table cellpadding="8" height="100%" width="100%"><tr><td valign="top"><br /="/"/><div><p style="BACKGROUND: #eaf5ff; MARGIN: 0pt; LINE-HEIGHT: 17pt"><span style="FONT-SIZE: 10.5pt; FONT-FAMILY: Verdana">It is easy to show: </span></p><p style="BACKGROUND: #eaf5ff; MARGIN: 0pt; LINE-HEIGHT: 17pt"><span style="FONT-SIZE: 10.5pt; FONT-FAMILY: Verdana"><strong>The sum of two consecutive odd integers that neither are divisible by 3 is divisible by 12.</strong></span></p><p style="BACKGROUND: #eaf5ff; MARGIN: 0pt; LINE-HEIGHT: 17pt"><span style="FONT-SIZE: 10.5pt; FONT-FAMILY: Verdana"><strong></strong></span> <span style="display:none;">www.ddhw.com</span></p><p style="BACKGROUND: #eaf5ff; MARGIN: 0pt; LINE-HEIGHT: 17pt"><span style="FONT-SIZE: 10.5pt; FONT-FAMILY: Verdana">Is it more general than the above-mentioned result ?</span></p></div><br /="/"/><br /="/"/> <div style="MARGIN-TOP:20px;MARGIN-LEFT:0;MARGIN-BOTTOM:0;float:left"></div></td></tr></table>回复：回复：Thanks. You are right.
<table cellpadding="8" height="100%" width="100%"><tr><td valign="top"><br /="/"/><div>I did not think about this way. Thank you again.</div><span style="display:none;">www.ddhw.com</span><br /="/"/><br /="/"/> <div style="MARGIN-TOP:20px;MARGIN-LEFT:0;MARGIN-BOTTOM:0;float:left"></div></td></tr></table>
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